QuestionFind the inverse function $f^{-1}(x)$ for $f(x) = 2x + 16$ . What is $f^{-1}(x)$ ?

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=x+16$ . We are asked to find the inverse of the function, denoted as $f^{-1}(x)$

STEP 2

The inverse of a function $f(x)$ is found by swapping $x$ and $y$ and solving for $y$ . So, we start by writing the function $f(x)$ as $y=2x+16$ .

STEP 3

Swap $x$ and $y$ in the equation.
$x=2y+16$

STEP 4

Now, we solve for $y$ to find the inverse function. First, subtract16 from both sides of the equation.
$x-16=2y$

STEP 5

Next, divide both sides of the equation by2 to isolate $y$ .
$y=\frac{x-16}{2}$

STEP 6

Finally, we replace $y$ with $f^{-1}(x)$ to denote that we have found the inverse function.
$f^{-1}(x)=\frac{x-16}{2}$ So, the inverse of the function $f(x)=2x+16$ is $f^{-1}(x)=\frac{x-16}{2}$ .

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QuestionFind the inverse function $f^{-1}(x)$ for $f(x) = 2x + 16$ . What is $f^{-1}(x)$ ?

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=x+16$ . We are asked to find the inverse of the function, denoted as $f^{-1}(x)$

STEP 2

The inverse of a function $f(x)$ is found by swapping $x$ and $y$ and solving for $y$ . So, we start by writing the function $f(x)$ as $y=2x+16$ .

STEP 3

Swap $x$ and $y$ in the equation.
$x=2y+16$

STEP 4

Now, we solve for $y$ to find the inverse function. First, subtract16 from both sides of the equation.
$x-16=2y$

STEP 5

Next, divide both sides of the equation by2 to isolate $y$ .
$y=\frac{x-16}{2}$

STEP 6

Finally, we replace $y$ with $f^{-1}(x)$ to denote that we have found the inverse function.
$f^{-1}(x)=\frac{x-16}{2}$ So, the inverse of the function $f(x)=2x+16$ is $f^{-1}(x)=\frac{x-16}{2}$ .

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QuestionFind the inverse function f−1(x)f^{-1}(x)f−1(x) for f(x)=2x+16f(x) = 2x + 16f(x)=2x+16. What is f−1(x)f^{-1}(x)f−1(x)?

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=x+16f(x)=x+16f(x)=x+16 . We are asked to find the inverse of the function, denoted as f−1(x)f^{-1}(x)f−1(x)

STEP 2

The inverse of a function f(x)f(x)f(x) is found by swapping xxx and yyy and solving for yyy. So, we start by writing the function f(x)f(x)f(x) as y=2x+16y=2x+16y=2x+16.

STEP 3

Swap xxx and yyy in the equation.x=2y+16x=2y+16x=2y+16

STEP 4

Now, we solve for yyy to find the inverse function. First, subtract16 from both sides of the equation.x−16=2yx-16=2yx−16=2y

STEP 5

Next, divide both sides of the equation by2 to isolate yyy.y=x−162y=\frac{x-16}{2}y=2x−16​

STEP 6

Finally, we replace yyy with f−1(x)f^{-1}(x)f−1(x) to denote that we have found the inverse function.f−1(x)=x−162f^{-1}(x)=\frac{x-16}{2}f−1(x)=2x−16​So, the inverse of the function f(x)=2x+16f(x)=2x+16f(x)=2x+16 is f−1(x)=x−162f^{-1}(x)=\frac{x-16}{2}f−1(x)=2x−16​.

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QuestionFind the inverse function $f^{-1}(x)$ for $f(x) = 2x + 16$ . What is $f^{-1}(x)$ ?

Assumptions1. The function is $f(x)=x+16$ . We are asked to find the inverse of the function, denoted as $f^{-1}(x)$

The inverse of a function $f(x)$ is found by swapping $x$ and $y$ and solving for $y$ . So, we start by writing the function $f(x)$ as $y=2x+16$ .

Swap $x$ and $y$ in the equation.
$x=2y+16$

Now, we solve for $y$ to find the inverse function. First, subtract16 from both sides of the equation.
$x-16=2y$

Next, divide both sides of the equation by2 to isolate $y$ .
$y=\frac{x-16}{2}$

Finally, we replace $y$ with $f^{-1}(x)$ to denote that we have found the inverse function.
$f^{-1}(x)=\frac{x-16}{2}$ So, the inverse of the function $f(x)=2x+16$ is $f^{-1}(x)=\frac{x-16}{2}$ .