QuestionFind the inverse of $f(x)=\frac{3 x}{5}+3$ . Which option is correct? A. $f^{-1}(x)=\frac{3(x+3)}{5}$ B. $f^{-1}(x)=\frac{5(x-3)}{3}$ C. $f^{-1}(x)=\frac{5(x-3)}{3}$ D. $f^{-1}(x)=\frac{3(x-3)}{5}$

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{3x}{5}+3$ . We need to find the inverse of the function $f(x)$

STEP 2

The inverse of a function $f(x)$ is denoted as $f^{-1}(x)$ . To find the inverse of a function, we switch the roles of $x$ and $y$ and then solve for $y$ .
So, we start by writing $f(x)$ as $y$ $y = \frac{x}{5} +$

STEP 3

Now, we switch the roles of $x$ and $y$ $x = \frac{3y}{5} +3$

STEP 4

We solve this equation for $y$ to find the inverse function. First, subtract3 from both sides $x -3 = \frac{3y}{}$

STEP 5

Then, multiply both sides by $\frac{5}{3}$ to isolate $y$ $y = \frac{5(x -3)}{3}$

STEP 6

So, the inverse of the function $f(x)$ is $f^{-1}(x) = \frac{5(x -3)}{3}$ . Comparing this with the given options, we see that the correct answer is option B.
The inverse of the function $f(x)=\frac{3x}{5}+3$ is $f^{-1}(x)=\frac{5(x-3)}{3}$ .

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QuestionFind the inverse of $f(x)=\frac{3 x}{5}+3$ . Which option is correct? A. $f^{-1}(x)=\frac{3(x+3)}{5}$ B. $f^{-1}(x)=\frac{5(x-3)}{3}$ C. $f^{-1}(x)=\frac{5(x-3)}{3}$ D. $f^{-1}(x)=\frac{3(x-3)}{5}$

Studdy Solution

STEP 1

Assumptions1. The function is $f(x)=\frac{3x}{5}+3$ . We need to find the inverse of the function $f(x)$

STEP 2

The inverse of a function $f(x)$ is denoted as $f^{-1}(x)$ . To find the inverse of a function, we switch the roles of $x$ and $y$ and then solve for $y$ .
So, we start by writing $f(x)$ as $y$ $y = \frac{x}{5} +$

STEP 3

Now, we switch the roles of $x$ and $y$ $x = \frac{3y}{5} +3$

STEP 4

We solve this equation for $y$ to find the inverse function. First, subtract3 from both sides $x -3 = \frac{3y}{}$

STEP 5

Then, multiply both sides by $\frac{5}{3}$ to isolate $y$ $y = \frac{5(x -3)}{3}$

STEP 6

So, the inverse of the function $f(x)$ is $f^{-1}(x) = \frac{5(x -3)}{3}$ . Comparing this with the given options, we see that the correct answer is option B.
The inverse of the function $f(x)=\frac{3x}{5}+3$ is $f^{-1}(x)=\frac{5(x-3)}{3}$ .

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Studdy Solution

STEP 1

Assumptions1. The function is f(x)=3x5+3f(x)=\frac{3x}{5}+3f(x)=53x​+3 . We need to find the inverse of the function f(x)f(x)f(x)

STEP 2

The inverse of a function f(x)f(x)f(x) is denoted as f−1(x)f^{-1}(x)f−1(x). To find the inverse of a function, we switch the roles of xxx and yyy and then solve for yyy.So, we start by writing f(x)f(x)f(x) as yyyy=x5+y = \frac{x}{5} +y=5x​+

STEP 3

Now, we switch the roles of xxx and yyyx=3y5+3x = \frac{3y}{5} +3x=53y​+3

STEP 4

We solve this equation for yyy to find the inverse function. First, subtract3 from both sidesx−3=3yx -3 = \frac{3y}{}x−3=3y​

STEP 5

Then, multiply both sides by 53\frac{5}{3}35​ to isolate yyyy=5(x−3)3y = \frac{5(x -3)}{3}y=35(x−3)​

STEP 6

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Assumptions1. The function is $f(x)=\frac{3x}{5}+3$ . We need to find the inverse of the function $f(x)$

The inverse of a function $f(x)$ is denoted as $f^{-1}(x)$ . To find the inverse of a function, we switch the roles of $x$ and $y$ and then solve for $y$ .
So, we start by writing $f(x)$ as $y$ $y = \frac{x}{5} +$

Now, we switch the roles of $x$ and $y$ $x = \frac{3y}{5} +3$

We solve this equation for $y$ to find the inverse function. First, subtract3 from both sides $x -3 = \frac{3y}{}$

Then, multiply both sides by $\frac{5}{3}$ to isolate $y$ $y = \frac{5(x -3)}{3}$