Intro to Inverse Functions

​Inverse Functions

Multiple Choice

What does an inverse function do?

• Nothing

• Makes it bigger

• Does the opposite of the original function

Multiple Choice

What does it mean to find the inverse of a function?

• the x's and y's are switched

• the x's and y's are divided by 2

• the x's and y's are made negative

• the x's and y's are the same

Multiple Choice

Generate the inverse of the function represented in the table.

Multiple Choice

Generate the inverse of the function represented in the table.

Multiple Choice

How do we find the inverse in a table?

• the x's and y's are switched

• the x's and y's are divided by 2

• the x's and y's are made negative

• the x's and y's are the same

Multiple Choice

If the equation of f(x) goes through (1, 4) and (4, 6), what points does f^-1(x) go through?

• (1, 4) and (4, 6)

• (-4, -1) and (-6, -4)

• (4, 1) and (6, 4)

Multiple Choice

The inverse of the function f(x) is written as ...

• f ^-1(x)
• f ²(x)
• f '(x)
• f ⁺(x)

Multiple Choice

Look at the steps. If we asked to find an inverse of

$$f\left(x\right)=\sqrt[]{x-5}+10$$ What would be the first step

• $$f\left(x\right)=\sqrt[]{x-5}+10$$

• $$y=\sqrt[]{x-5}+10$$

• $$y+10=\sqrt[]{x-5}$$

Multiple Choice

The first step was $$y=\sqrt[]{x-5}+10$$

What would be the second step?

• $$x=\sqrt[]{y-5}+10$$

• $$y-10=\sqrt[]{x-5}$$

• f(x)=x³

Multiple Choice

Step 3. Our new equation is $$x=\sqrt[]{y-5}+10$$ solve for y. How would you start?

• add 10 to both sides

• subtract 10 from both sides

• divide by 10

Multiple Choice

Step 3. Now we have $$x-10=\sqrt[]{y-5}$$ What would you do to solve for y?

• Square both sides

• add 5

• take a square root of both sides

Multiple Choice

Step 3. Now we have $$\left(x-10\right)^2=y-5$$ What would you do to solve for y?

• subtract 5

• add 5

• take a square root of both sides