3 is good
4:
let y = (x+5)^2
interchange x with y
x = (y+5)^2
+-sqrt(x) = y+5
y = -5 +-sqrt(x) or f(x) = -5 +-sqrt(x)
3.) f(x)= 2x-5 for this one I have
y= (x+5)/2 is this correct?
4.) g(x)= (x+5)^3
I am stuck on this one.
4:
let y = (x+5)^2
interchange x with y
x = (y+5)^2
+-sqrt(x) = y+5
y = -5 +-sqrt(x) or f(x) = -5 +-sqrt(x)
I just have one question for 4.) the problem is g(x)= (x+5)^3
how were you able to convert the equation to the following?
let y = (x+5)^2
interchange x with y
x = (y+5)^2
so just change the sqrt to cube root and use only the positive sign.
so last line should be
y = -5 +-cuberoot(x)
For function f(x) = 2x - 5:
Step 1: Replace f(x) with y: y = 2x - 5.
Step 2: Swap x and y: x = 2y - 5.
Step 3: Solve for y: Add 5 to both sides of the equation to isolate 2y: x + 5 = 2y.
Step 4: Divide both sides of the equation by 2 to solve for y: (x + 5) / 2 = y.
Therefore, the inverse of function f(x) = 2x - 5 is y = (x + 5) / 2.
Now let's move on to function g(x) = (x + 5)^3:
Step 1: Replace g(x) with y: y = (x + 5)^3.
Step 2: Swap x and y: x = (y + 5)^3.
At this point, finding a formula for the inverse of this function becomes more challenging. Instead of trying to solve the equation directly, we can use a different approach.
Step 3: Take the cube root of both sides to eliminate the power of 3: ∛(x) = ∛((y + 5)^3).
Step 4: Simplify the right side: ∛(x) = y + 5.
Step 5: Subtract 5 from both sides of the equation to solve for y: ∛(x) - 5 = y.
Therefore, the inverse of function g(x) = (x + 5)^3 is y = ∛(x) - 5.
Please note that when finding the inverse of a function, it is crucial to verify if the inverse is indeed a valid function by checking if it passes the horizontal line test.