SOLUTION: What is the inverse function of f(x)=sqrt(5+8x)?

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Question 1167054: What is the inverse function of f(x)=sqrt(5+8x)?
Found 2 solutions by Boreal, greenestamps:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
y=sqrt(5+8x), and the domain is x=-5/8
x=sqrt(5+8y)
x^2=5+8y
8y=x^2-5
y=(1/8)(x^2-5) with the range restricted to the domain x>=-5/8
graph%28300%2C300%2C-2%2C10%2C-10%2C10%2Csqrt%285%2B8x%29%2C%281%2F8%29%28x%5E2-5%29%29

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


This function is one for which there is an easy alternative to the standard method for finding an inverse.

The given function does the following to the input:
(1) multiply by 8
(2) add 5
(3) take the square root

The inverse function has to "get you back where you started"; to do that, it has to perform the opposite operations on the input, in the reverse order:
(1) square it x%5E2
(2) subtract 5 x%5E2-5
(3) divide by 8 %28x%5E2-5%29%2F8

The inverse function is

f%28x%29+=+%28x%5E2-5%29%2F8

Of course the domain of the function is restricted by the restriction on the domain of the given function.