QuestionFind the inverse function $f^{-1}(x)$ if $f(x) = \frac{x}{4} - 5$ . What is $f^{-1}(x) = [?] x + []$ ?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x)=\frac{x}{4}-5$ . We are to find the inverse of this function, denoted by $f^{-1}(x)$

STEP 2

To find the inverse of a function, we first replace $f(x)$ with $y$ .
$y=\frac{x}{4}-5$

STEP 3

Next, we switch the roles of $x$ and $y$ . This means we replace $y$ with $x$ and $x$ with $y$ in the equation.
$x=\frac{y}{}-5$

STEP 4

Now, we solve this equation for $y$ to get the inverse function $f^{-1}(x)$ . First, we isolate the term with $y$ by adding to both sides of the equation.
$x+=\frac{y}{4}$

STEP 5

Finally, we multiply both sides of the equation by4 to solve for $y$ .
$4(x+5)=y$ So, the inverse function is $f^{-1}(x)=4x+20$ .

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QuestionFind the inverse function $f^{-1}(x)$ if $f(x) = \frac{x}{4} - 5$ . What is $f^{-1}(x) = [?] x + []$ ?

Studdy Solution

STEP 1

Assumptions1. The function $f(x)$ is given by $f(x)=\frac{x}{4}-5$ . We are to find the inverse of this function, denoted by $f^{-1}(x)$

STEP 2

To find the inverse of a function, we first replace $f(x)$ with $y$ .
$y=\frac{x}{4}-5$

STEP 3

Next, we switch the roles of $x$ and $y$ . This means we replace $y$ with $x$ and $x$ with $y$ in the equation.
$x=\frac{y}{}-5$

STEP 4

Now, we solve this equation for $y$ to get the inverse function $f^{-1}(x)$ . First, we isolate the term with $y$ by adding to both sides of the equation.
$x+=\frac{y}{4}$

STEP 5

Finally, we multiply both sides of the equation by4 to solve for $y$ .
$4(x+5)=y$ So, the inverse function is $f^{-1}(x)=4x+20$ .

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QuestionFind the inverse function f−1(x)f^{-1}(x)f−1(x) if f(x)=x4−5f(x) = \frac{x}{4} - 5f(x)=4x​−5. What is f−1(x)=[?]x+[]f^{-1}(x) = [?] x + []f−1(x)=[?]x+[]?

Studdy Solution

STEP 1

Assumptions1. The function f(x)f(x)f(x) is given by f(x)=x4−5f(x)=\frac{x}{4}-5f(x)=4x​−5 . We are to find the inverse of this function, denoted by f−1(x)f^{-1}(x)f−1(x)

STEP 2

To find the inverse of a function, we first replace f(x)f(x)f(x) with yyy.y=x4−5y=\frac{x}{4}-5y=4x​−5

STEP 3

Next, we switch the roles of xxx and yyy. This means we replace yyy with xxx and xxx with yyy in the equation.x=y−5x=\frac{y}{}-5x=y​−5

STEP 4

Now, we solve this equation for yyy to get the inverse function f−1(x)f^{-1}(x)f−1(x). First, we isolate the term with yyy by adding to both sides of the equation.x+=y4x+=\frac{y}{4}x+=4y​

STEP 5

Finally, we multiply both sides of the equation by4 to solve for yyy.4(x+5)=y4(x+5)=y4(x+5)=ySo, the inverse function is f−1(x)=4x+20f^{-1}(x)=4x+20f−1(x)=4x+20.

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QuestionFind the inverse function $f^{-1}(x)$ if $f(x) = \frac{x}{4} - 5$ . What is $f^{-1}(x) = [?] x + []$ ?

Assumptions1. The function $f(x)$ is given by $f(x)=\frac{x}{4}-5$ . We are to find the inverse of this function, denoted by $f^{-1}(x)$

To find the inverse of a function, we first replace $f(x)$ with $y$ .
$y=\frac{x}{4}-5$

Next, we switch the roles of $x$ and $y$ . This means we replace $y$ with $x$ and $x$ with $y$ in the equation.
$x=\frac{y}{}-5$

Now, we solve this equation for $y$ to get the inverse function $f^{-1}(x)$ . First, we isolate the term with $y$ by adding to both sides of the equation.
$x+=\frac{y}{4}$

Finally, we multiply both sides of the equation by4 to solve for $y$ .
$4(x+5)=y$ So, the inverse function is $f^{-1}(x)=4x+20$ .