Question

Find the inverse of lower f left parenthesis x right parenthesis equals negative Start Root 3 x minus 27 End Root

Answer 1

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.

Answer 2

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

Answer 3

The correct answer choice is:

f^(-1)(x) = (1/3)x^2 + 9, x ≥ 0

Answer 4

thats wrong

Answer 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

Answer 6

thats not an option

Answer 7

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

Answer 8

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 9

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.

Answer 10

wrong

Answer 11

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.

Answer 12

its either a or c?

Answer 13

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.

Answer 14

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

Answer 15

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, ∞)