QuestionFind $f^{-1}(9)$ given that $\mathrm{f}(1)=9$ .

Studdy Solution

STEP 1

Assumptions1. The function f is invertible, meaning there exists a function $f^{-1}$ such that $f^{-1}(f(x))=x$ for all x in the domain of f, and $f(f^{-1}(x))=x$ for all x in the range of f. . We are given that $f(1)=9$ .

STEP 2

The value of $f^{-1}(9)$ is the value that, when input into the function f, yields9. According to the definition of an inverse function, this is the same as the input that yields9 when input into the function f.

STEP 3

We know from the given information that when we input1 into the function f, we get9. Therefore, when we input9 into the inverse function $f^{-1}$ , we should get1.
$f^{-1}(9) =1$ So, $f^{-1}(9) =1$ .

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