Question

F(x)=√x - 8. Find f¹(x) and its domain.

Answer 1

The inverse function is $f^{-1} = (x + 8)^2$, and the domain is the set of all real numbers equal to or larger than -8. So the correct option is C.

How to find the inverse function?

Remember that two functions are inverses if and only if:

$f( f^{-1}(x)) = x\\f^{-1}(f(x)) = x$

Here we have:

$f(x) = \sqrt{x} - 8$

Then we want to have:

$f(f^{-1}(x)) = \sqrt{f^{-1}(x)} - 8 = x$

Solving that for the inverse function, we get:

$f^{-1} = (x + 8)^2$

Now, how to get the domain. The domain of the inverse function is equal to the range of the original function.

$f(x) = \sqrt{x} - 8$

The range of f(x) is the set of all real numbers larger or equal than -8 (because the smallest value that x can take is 0).

Then the domain of the inverse function is the set of all real numbers equal to or larger than -8.

The correct option is C.

If you want to learn more about inverse functions:

brainly.com/question/14391067

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