Objective 4 - Inverse

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Find the inverse of a function, if it exists.

Link to section in online textbook

First, watch this video to learn when a function has an inverse and how to find the inverse of a function. Feel free to pause the video and fill out the notes as you go.

Determine whether the function below is 1-1.

$f(x) = \sage {f1}$

$\answer [format=string]{Yes}$

“Yes” or “No”.

If $f(x)$ is 1-1, find the inverse and define the domain on which the inverse is valid. If $f(x)$ is not 1-1, put “NA” for all answer blocks.

$f^{-1}(x) = \answer {\sage {f1Inverse}}$

To find the inverse of a function, switch $x$ and $y$ , then solve for $y$ . Don’t round.

Domain of $f^{-1}(x)$ : $\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

Think about the shape of the original function: are there places whether the function is not defined?

Determine whether the function below is 1-1.

$f(x) = \sage {f2}$

$\answer [format=string]{No}$

“Yes” or “No”.

If $f(x)$ is 1-1, find the inverse and define the domain on which the inverse is valid. If $f(x)$ is not 1-1, put “NA” for all answer blocks.

$f^{-1}(x) = \answer [format=string]{NA}$

To find the inverse of a function, switch $x$ and $y$ , then solve for $y$ . Don’t round.

Domain of $f^{-1}(x)$ : $\answer [format=string]{NA} \answer [format=string]{NA}, \answer [format=string]{NA} \answer [format=string]{NA}$

Think about the shape of the original function: are there places whether the function is not defined?

Determine whether the function below is 1-1.

$f(x) = \sage {f3}$

$\answer [format=string]{Yes}$

“Yes” or “No”.

If $f(x)$ is 1-1, find the inverse and define the domain on which the inverse is valid. If $f(x)$ is not 1-1, put “NA” for all answer blocks.

$f^{-1}(x) = \answer {\sage {f3Inverse}}$

To find the inverse of a function, switch $x$ and $y$ , then solve for $y$ . Don’t round.

Domain of $f^{-1}(x)$ : $\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

Think about the shape of the original function: are there places whether the function is not defined?

Determine whether the function below is 1-1.

$f(x) = \sage {f4}$

$\answer [format=string]{Yes}$

“Yes” or “No”.

If $f(x)$ is 1-1, find the inverse and define the domain on which the inverse is valid. If $f(x)$ is not 1-1, put “NA” for all answer blocks.

$f^{-1}(x) = \answer {\sage {f4Inverse}}$

To find the inverse of a function, switch $x$ and $y$ , then solve for $y$ . Don’t round.

Domain of $f^{-1}(x)$ : $\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer {\sage {domain4[1]}} \answer [format=string]{]}$

Think about the shape of the original function: are there places whether the function is not defined?

Determine whether the function below is 1-1.

$f(x) = \sage {f5}$

$\answer [format=string]{Yes}$

“Yes” or “No”.

If $f(x)$ is 1-1, find the inverse and define the domain on which the inverse is valid. If $f(x)$ is not 1-1, put “NA” for all answer blocks.

$f^{-1}(x) = \answer {\sage {f5Inverse}}$

To find the inverse of a function, switch $x$ and $y$ , then solve for $y$ . Don’t round.

Domain of $f^{-1}(x)$ : $\answer [format=string]{(} \answer {\sage {-Infinity}}, \answer {\sage {Infinity}} \answer [format=string]{)}$

Think about the shape of the original function: are there places whether the function is not defined?