QuestionFind the inverse of the function $f(x)=3x+9$ . What is $f^{-1}(x)=\frac{x}{[?]}+$ ?

Studdy Solution

STEP 1

Assumptions1. The function is $f(x) =3x +9$ . We are asked to find the inverse function, denoted as $f^{-1}(x)$

STEP 2

The first step to find the inverse of a function is to replace the function notation $f(x)$ with $y$ .
$y =x +9$

STEP 3

Next, we swap $x$ and $y$ . This means we replace every $x$ in our equation with $y$ and vice versa.
$x =3y +9$

STEP 4

Now, we solve this equation for $y$ to find the inverse function. First, subtract9 from both sides of the equation.
$x -9 =3y$

STEP 5

Finally, divide both sides of the equation by3 to solve for $y$ .
$y = \frac{x -9}{3}$

STEP 6

Now that we have solved for $y$ , we can write our answer in terms of $f^{-1}(x)$ .
$f^{-1}(x) = \frac{x -9}{3}$ So, the inverse function of $f(x) =3x +9$ is $f^{-1}(x) = \frac{x -9}{3}$ .

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QuestionFind the inverse of the function $f(x)=3x+9$ . What is $f^{-1}(x)=\frac{x}{[?]}+$ ?

Studdy Solution

STEP 1

Assumptions1. The function is $f(x) =3x +9$ . We are asked to find the inverse function, denoted as $f^{-1}(x)$

STEP 2

The first step to find the inverse of a function is to replace the function notation $f(x)$ with $y$ .
$y =x +9$

STEP 3

Next, we swap $x$ and $y$ . This means we replace every $x$ in our equation with $y$ and vice versa.
$x =3y +9$

STEP 4

Now, we solve this equation for $y$ to find the inverse function. First, subtract9 from both sides of the equation.
$x -9 =3y$

STEP 5

Finally, divide both sides of the equation by3 to solve for $y$ .
$y = \frac{x -9}{3}$

STEP 6

Now that we have solved for $y$ , we can write our answer in terms of $f^{-1}(x)$ .
$f^{-1}(x) = \frac{x -9}{3}$ So, the inverse function of $f(x) =3x +9$ is $f^{-1}(x) = \frac{x -9}{3}$ .

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QuestionFind the inverse of the function f(x)=3x+9f(x)=3x+9f(x)=3x+9. What is f−1(x)=x[?]+f^{-1}(x)=\frac{x}{[?]}+f−1(x)=[?]x​+?

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=3x+9f(x) =3x +9f(x)=3x+9 . We are asked to find the inverse function, denoted as f−1(x)f^{-1}(x)f−1(x)

STEP 2

The first step to find the inverse of a function is to replace the function notation f(x)f(x)f(x) with yyy.y=x+9y =x +9y=x+9

STEP 3

Next, we swap xxx and yyy. This means we replace every xxx in our equation with yyy and vice versa.x=3y+9x =3y +9x=3y+9

STEP 4

Now, we solve this equation for yyy to find the inverse function. First, subtract9 from both sides of the equation.x−9=3yx -9 =3yx−9=3y

STEP 5

Finally, divide both sides of the equation by3 to solve for yyy.y=x−93y = \frac{x -9}{3}y=3x−9​

STEP 6

Now that we have solved for yyy, we can write our answer in terms of f−1(x)f^{-1}(x)f−1(x).f−1(x)=x−93f^{-1}(x) = \frac{x -9}{3}f−1(x)=3x−9​So, the inverse function of f(x)=3x+9f(x) =3x +9f(x)=3x+9 is f−1(x)=x−93f^{-1}(x) = \frac{x -9}{3}f−1(x)=3x−9​.

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QuestionFind the inverse of the function $f(x)=3x+9$ . What is $f^{-1}(x)=\frac{x}{[?]}+$ ?

Assumptions1. The function is $f(x) =3x +9$ . We are asked to find the inverse function, denoted as $f^{-1}(x)$

The first step to find the inverse of a function is to replace the function notation $f(x)$ with $y$ .
$y =x +9$

Next, we swap $x$ and $y$ . This means we replace every $x$ in our equation with $y$ and vice versa.
$x =3y +9$

Now, we solve this equation for $y$ to find the inverse function. First, subtract9 from both sides of the equation.
$x -9 =3y$

Finally, divide both sides of the equation by3 to solve for $y$ .
$y = \frac{x -9}{3}$

Now that we have solved for $y$ , we can write our answer in terms of $f^{-1}(x)$ .
$f^{-1}(x) = \frac{x -9}{3}$ So, the inverse function of $f(x) =3x +9$ is $f^{-1}(x) = \frac{x -9}{3}$ .