Question
Find the inverse of lower f left parenthesis x right parenthesis equals negative Start Root 3 x minus 27 End Root
Answers
Answer
answer choices
Responses
lower f superscript negative 1 baseline left parenthesis x right parenthesis equals negative Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x greater-than-or-equal-to 0
lower f superscript negative 1 baseline left parenthesis x right parenthesis equals negative Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x Element-of bold upper R
lower f superscript negative 1 baseline left parenthesis x right parenthesis equals Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x less-than-or-equal-to 0
lower f superscript negative 1 baseline left parenthesis x right parenthesis equals Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x greater-than-or-equal-to 0
Responses
lower f superscript negative 1 baseline left parenthesis x right parenthesis equals negative Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x greater-than-or-equal-to 0
lower f superscript negative 1 baseline left parenthesis x right parenthesis equals negative Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x Element-of bold upper R
lower f superscript negative 1 baseline left parenthesis x right parenthesis equals Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x less-than-or-equal-to 0
lower f superscript negative 1 baseline left parenthesis x right parenthesis equals Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x greater-than-or-equal-to 0
Answer
thats wrong
Answer
thats not an option
Answer
Responses
a) lower f superscript negative 1 baseline left parenthesis x right parenthesis equals negative Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x greater-than-or-equal-to 0
Image with alt text: lower f superscript negative 1 baseline left parenthesis x right parenthesis equals negative Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x greater-than-or-equal-to 0
b) lower f superscript negative 1 baseline left parenthesis x right parenthesis equals negative Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x Element-of bold upper R
Image with alt text: lower f superscript negative 1 baseline left parenthesis x right parenthesis equals negative Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x Element-of bold upper R
c) lower f superscript negative 1 baseline left parenthesis x right parenthesis equals Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x less-than-or-equal-to 0
Image with alt text: lower f superscript negative 1 baseline left parenthesis x right parenthesis equals Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x less-than-or-equal-to 0
d) lower f superscript negative 1 baseline left parenthesis x right parenthesis equals Start Fraction 1 over 3 End Fraction baseline x superscript 2 baseline plus 9 comma x greater-than-or-equal-to 0
Answer
wrong
Answer
its either a or c?
Answer
Find the domain of the function. Write the answer in interval notation.
lower f left parenthesis x right parenthesis equals Start Fraction 1 over x superscript 2 baseline minus 0.01 End Fraction
lower f left parenthesis x right parenthesis equals Start Fraction 1 over x superscript 2 baseline minus 0.01 End Fraction
Answered by
GPT 3.5
To find the inverse of a function, we need to switch the roles of x and y and solve for y.
Given: f(x) = -√(3x - 27)
1. Swap x and y: x = -√(3y - 27)
2. Square both sides to eliminate the square root: x^2 = 3y - 27
3. Add 27 to both sides: x^2 + 27 = 3y
4. Divide both sides by 3: (x^2 + 27)/3 = y
5. Simplify the expression: y = (x^2 + 27)/3
Therefore, the inverse of f(x) = -√(3x - 27) is f^(-1)(x) = (x^2 + 27)/3.
Given: f(x) = -√(3x - 27)
1. Swap x and y: x = -√(3y - 27)
2. Square both sides to eliminate the square root: x^2 = 3y - 27
3. Add 27 to both sides: x^2 + 27 = 3y
4. Divide both sides by 3: (x^2 + 27)/3 = y
5. Simplify the expression: y = (x^2 + 27)/3
Therefore, the inverse of f(x) = -√(3x - 27) is f^(-1)(x) = (x^2 + 27)/3.
Answered by
GPT 3.5
The correct answer choice is:
f^(-1)(x) = (1/3)x^2 + 9, x ≥ 0
f^(-1)(x) = (1/3)x^2 + 9, x ≥ 0
Answered by
GPT 3.5
Apologies for the incorrect response. Let's find the correct inverse.
Given: f(x) = -√(3x - 27)
1. Swap x and y: x = -√(3y - 27)
2. Square both sides to eliminate the square root: x^2 = 3y - 27
3. Add 27 to both sides: x^2 + 27 = 3y
4. Divide both sides by 3: (x^2 + 27)/3 = y
Therefore, the correct inverse of f(x) = -√(3x - 27) is:
f^(-1)(x) = (x^2 + 27)/3
Given: f(x) = -√(3x - 27)
1. Swap x and y: x = -√(3y - 27)
2. Square both sides to eliminate the square root: x^2 = 3y - 27
3. Add 27 to both sides: x^2 + 27 = 3y
4. Divide both sides by 3: (x^2 + 27)/3 = y
Therefore, the correct inverse of f(x) = -√(3x - 27) is:
f^(-1)(x) = (x^2 + 27)/3
Answered by
GPT 3.5
Apologies for the confusion. Let's try again.
Given: f(x) = -√(3x - 27)
To find the inverse, we need to switch x and y and solve for y.
1. Swap x and y: x = -√(3y - 27)
2. Square both sides to eliminate the square root: x^2 = 3y - 27
3. Add 27 to both sides: x^2 + 27 = 3y
4. Divide both sides by 3: (x^2 + 27)/3 = y
The correct answer choice for the inverse function is:
f^(-1)(x) = (x^2 + 27)/3, x ≥ 0
Given: f(x) = -√(3x - 27)
To find the inverse, we need to switch x and y and solve for y.
1. Swap x and y: x = -√(3y - 27)
2. Square both sides to eliminate the square root: x^2 = 3y - 27
3. Add 27 to both sides: x^2 + 27 = 3y
4. Divide both sides by 3: (x^2 + 27)/3 = y
The correct answer choice for the inverse function is:
f^(-1)(x) = (x^2 + 27)/3, x ≥ 0
Answered by
GPT 3.5
I apologize for the previous mistakes. The correct answer is:
b) f^(-1)(x) = (1/3)x^2 + 9, x ∈ ℝ
This means that the inverse of f(x) is given by the function (1/3)x^2 + 9, and x can be any real number.
b) f^(-1)(x) = (1/3)x^2 + 9, x ∈ ℝ
This means that the inverse of f(x) is given by the function (1/3)x^2 + 9, and x can be any real number.
Answered by
GPT 3.5
Apologies for the confusion. Let's try again.
Given: f(x) = -√(3x - 27)
To find the inverse, we need to switch x and y and solve for y.
1. Swap x and y: x = -√(3y - 27)
2. Square both sides to eliminate the square root: x^2 = 3y - 27
3. Add 27 to both sides: x^2 + 27 = 3y
4. Divide both sides by 3: (x^2 + 27)/3 = y
The correct answer choice for the inverse function is:
f^(-1)(x) = (x^2 + 27)/3, for all real values of x.
Given: f(x) = -√(3x - 27)
To find the inverse, we need to switch x and y and solve for y.
1. Swap x and y: x = -√(3y - 27)
2. Square both sides to eliminate the square root: x^2 = 3y - 27
3. Add 27 to both sides: x^2 + 27 = 3y
4. Divide both sides by 3: (x^2 + 27)/3 = y
The correct answer choice for the inverse function is:
f^(-1)(x) = (x^2 + 27)/3, for all real values of x.
Answered by
GPT 3.5
I apologize for the confusion. Based on the responses you provided, the correct answer is:
c) f^(-1)(x) = (1/3)x^2 + 9, x ≤ 0
This means that the inverse of f(x) is given by the function (1/3)x^2 + 9, and x is less than or equal to 0.
c) f^(-1)(x) = (1/3)x^2 + 9, x ≤ 0
This means that the inverse of f(x) is given by the function (1/3)x^2 + 9, and x is less than or equal to 0.
Answered by
GPT 3.5
To find the domain of the function f(x) = 1/(x^2 - 0.01), we need to determine the values of x for which the function is defined.
Since division by zero is undefined, we need to make sure that the denominator, x^2 - 0.01, is not equal to zero.
So, x^2 - 0.01 ≠ 0
Solving this equation, we get:
x^2 ≠ 0.01
Taking the square root of both sides, we have:
x ≠ ±0.1
Therefore, the domain of the function f(x) is all real numbers except x = 0.1 and x = -0.1.
In interval notation, the domain is written as:
(-∞, -0.1) U (-0.1, 0.1) U (0.1, ∞)
Since division by zero is undefined, we need to make sure that the denominator, x^2 - 0.01, is not equal to zero.
So, x^2 - 0.01 ≠ 0
Solving this equation, we get:
x^2 ≠ 0.01
Taking the square root of both sides, we have:
x ≠ ±0.1
Therefore, the domain of the function f(x) is all real numbers except x = 0.1 and x = -0.1.
In interval notation, the domain is written as:
(-∞, -0.1) U (-0.1, 0.1) U (0.1, ∞)
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