QuestionFind the inverse of the function $f(x)=2x+1$ .

Studdy Solution

STEP 1

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

STEP 2

To find the inverse of a function, we first replace the function notation $f(x)$ with $y$ . This gives us $y =2x +1$

STEP 3

The next step in finding the inverse of a function is to swap $x$ and $y$ . This gives us $x =2y +1$

STEP 4

Now, we need to solve for $y$ to get the inverse function. First, subtract1 from both sides of the equation $x -1 =2y$

STEP 5

Finally, divide both sides of the equation by2 to solve for $y$ $y = \frac{x -1}{2}$

STEP 6

The last step is to replace $y$ with the notation for the inverse function, $f^{-1}(x)$ $f^{-1}(x) = \frac{x -1}{2}$ So, the inverse of the function $f(x)=2x+1$ is $f^{-1}(x)=\frac{x -1}{2}$ .

Was this helpful?

QuestionFind the inverse of the function $f(x)=2x+1$ .

Studdy Solution

STEP 1

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

STEP 2

To find the inverse of a function, we first replace the function notation $f(x)$ with $y$ . This gives us $y =2x +1$

STEP 3

The next step in finding the inverse of a function is to swap $x$ and $y$ . This gives us $x =2y +1$

STEP 4

Now, we need to solve for $y$ to get the inverse function. First, subtract1 from both sides of the equation $x -1 =2y$

STEP 5

Finally, divide both sides of the equation by2 to solve for $y$ $y = \frac{x -1}{2}$

STEP 6

The last step is to replace $y$ with the notation for the inverse function, $f^{-1}(x)$ $f^{-1}(x) = \frac{x -1}{2}$ So, the inverse of the function $f(x)=2x+1$ is $f^{-1}(x)=\frac{x -1}{2}$ .

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the inverse of the function f(x)=2x+1f(x)=2x+1f(x)=2x+1.

Studdy Solution

STEP 1

Assumptions1. The function is f(x)=x+1f(x)=x+1f(x)=x+1 . We are looking for the inverse of this function

STEP 2

To find the inverse of a function, we first replace the function notation f(x)f(x)f(x) with yyy. This gives usy=2x+1y =2x +1y=2x+1

STEP 3

The next step in finding the inverse of a function is to swap xxx and yyy. This gives usx=2y+1x =2y +1x=2y+1

STEP 4

Now, we need to solve for yyy to get the inverse function. First, subtract1 from both sides of the equationx−1=2yx -1 =2yx−1=2y

STEP 5

Finally, divide both sides of the equation by2 to solve for yyyy=x−12y = \frac{x -1}{2}y=2x−1​

STEP 6

The last step is to replace yyy with the notation for the inverse function, f−1(x)f^{-1}(x)f−1(x)f−1(x)=x−12f^{-1}(x) = \frac{x -1}{2}f−1(x)=2x−1​So, the inverse of the function f(x)=2x+1f(x)=2x+1f(x)=2x+1 is f−1(x)=x−12f^{-1}(x)=\frac{x -1}{2}f−1(x)=2x−1​.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionFind the inverse of the function $f(x)=2x+1$ .

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

To find the inverse of a function, we first replace the function notation $f(x)$ with $y$ . This gives us $y =2x +1$

The next step in finding the inverse of a function is to swap $x$ and $y$ . This gives us $x =2y +1$

Now, we need to solve for $y$ to get the inverse function. First, subtract1 from both sides of the equation $x -1 =2y$

Finally, divide both sides of the equation by2 to solve for $y$ $y = \frac{x -1}{2}$

The last step is to replace $y$ with the notation for the inverse function, $f^{-1}(x)$ $f^{-1}(x) = \frac{x -1}{2}$ So, the inverse of the function $f(x)=2x+1$ is $f^{-1}(x)=\frac{x -1}{2}$ .