QuestionFind the inverse of the function $f(x)=\frac{1}{9} x+2$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{1}{9} x+$ . We are looking for the inverse of this function

STEP 2

To find the inverse of a function, we first replace $f(x)$ with $y$ .
$y = \frac{1}{9} x +2$

STEP 3

Next, we switch the roles of $x$ and $y$ . This means we replace every $x$ with $y$ and every $y$ with $x$ .
$x = \frac{1}{9} y +2$

STEP 4

Now, we solve for $y$ to get the inverse function. First, subtract2 from both sides.
$x -2 = \frac{1}{9} y$

STEP 5

To isolate $y$ , multiply both sides by9.
$9(x -2) = y$

STEP 6

implify the equation to get the inverse function.
$y =9x -18$

STEP 7

Finally, replace $y$ with $f^{-1}(x)$ to denote the inverse function.
$f^{-1}(x) =9x -18$ The inverse of the function $f(x)=\frac{1}{9} x+2$ is $f^{-1}(x) =9x -18$ .

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QuestionFind the inverse of the function $f(x)=\frac{1}{9} x+2$ .

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{1}{9} x+$ . We are looking for the inverse of this function

STEP 2

To find the inverse of a function, we first replace $f(x)$ with $y$ .
$y = \frac{1}{9} x +2$

STEP 3

Next, we switch the roles of $x$ and $y$ . This means we replace every $x$ with $y$ and every $y$ with $x$ .
$x = \frac{1}{9} y +2$

STEP 4

Now, we solve for $y$ to get the inverse function. First, subtract2 from both sides.
$x -2 = \frac{1}{9} y$

STEP 5

To isolate $y$ , multiply both sides by9.
$9(x -2) = y$

STEP 6

implify the equation to get the inverse function.
$y =9x -18$

STEP 7

Finally, replace $y$ with $f^{-1}(x)$ to denote the inverse function.
$f^{-1}(x) =9x -18$ The inverse of the function $f(x)=\frac{1}{9} x+2$ is $f^{-1}(x) =9x -18$ .

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QuestionFind the inverse of the function f(x)=19x+2f(x)=\frac{1}{9} x+2f(x)=91​x+2.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=19x+f(x)=\frac{1}{9} x+f(x)=91​x+ . We are looking for the inverse of this function

STEP 2

To find the inverse of a function, we first replace f(x)f(x)f(x) with yyy.y=19x+2y = \frac{1}{9} x +2y=91​x+2

STEP 3

Next, we switch the roles of xxx and yyy. This means we replace every xxx with yyy and every yyy with xxx.x=19y+2x = \frac{1}{9} y +2x=91​y+2

STEP 4

Now, we solve for yyy to get the inverse function. First, subtract2 from both sides.x−2=19yx -2 = \frac{1}{9} yx−2=91​y

STEP 5

To isolate yyy, multiply both sides by9.9(x−2)=y9(x -2) = y9(x−2)=y

STEP 6

implify the equation to get the inverse function.y=9x−18y =9x -18y=9x−18

STEP 7

Finally, replace yyy with f−1(x)f^{-1}(x)f−1(x) to denote the inverse function.f−1(x)=9x−18f^{-1}(x) =9x -18f−1(x)=9x−18The inverse of the function f(x)=19x+2f(x)=\frac{1}{9} x+2f(x)=91​x+2 is f−1(x)=9x−18f^{-1}(x) =9x -18f−1(x)=9x−18.

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QuestionFind the inverse of the function $f(x)=\frac{1}{9} x+2$ .

Assumptions1. The function is $f(x)=\frac{1}{9} x+$ . We are looking for the inverse of this function

To find the inverse of a function, we first replace $f(x)$ with $y$ .
$y = \frac{1}{9} x +2$

Next, we switch the roles of $x$ and $y$ . This means we replace every $x$ with $y$ and every $y$ with $x$ .
$x = \frac{1}{9} y +2$

Now, we solve for $y$ to get the inverse function. First, subtract2 from both sides.
$x -2 = \frac{1}{9} y$

To isolate $y$ , multiply both sides by9.
$9(x -2) = y$

implify the equation to get the inverse function.
$y =9x -18$

Finally, replace $y$ with $f^{-1}(x)$ to denote the inverse function.
$f^{-1}(x) =9x -18$ The inverse of the function $f(x)=\frac{1}{9} x+2$ is $f^{-1}(x) =9x -18$ .