QuestionFind the inverse function $f^{-1}(x)$ for $f(x)=x+7$ and calculate $f^{-1}(-2)$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=x+7$ . We need to find the inverse of the function, $f^{-1}(x)$ 3. We are asked to find the value of $f^{-1}(-)$

STEP 2

The inverse of a function $f(x)$ , denoted as $f^{-1}(x)$ , is the function that reverses the operation of $f(x)$ . To find the inverse of $f(x)$ , we need to switch $x$ and $y$ and solve for $y$ .
Let $y = f(x)$ , so we have $y = x +7$ .

STEP 3

Switch $x$ and $y$ to find the inverse.
$x = y +7$

STEP 4

olve the equation for $y$ to find $f^{-1}(x)$ .
$y = x -7$ So, $f^{-1}(x) = x -7$ .

STEP 5

Now that we have the inverse function, we can find $f^{-1}(-2)$ by substituting $-2$ for $x$ in the inverse function.
$f^{-1}(-2) = -2 -7$

STEP 6

Calculate the value of $f^{-1}(-2)$ .
$f^{-1}(-2) = -2 - = -9$ So, $f^{-1}(-2) = -9$ .

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