Composition and Inverse Radical Functions

How are the graphs of a function and its inverse related?

• The graphs are symmetric about the y-axis.

• The graphs are symmetric about the x-axis.

• The graphs are symmetric about the line y = x.

• The graphs are identical.

What's the name of the inverse of g(x)?

• f(x)
• f^-1(x)
• y
• g^-1(x)

Are the following inverses of each other?

• True
• False

Find the inverse of f(x) = x² - 5

• f^-1(x) = √(x) + 5
• f^-1(x) = ∛(x-5)
• f^-1(x) =√(x+5)
• f^-1(x) = x² - 5

Find the inverse of the function including any restriction on domain

• f^-1 = x³ − 5, x ≥ 5
• f^-1 = x³ + 5,  x ≥ 0
• f^-1 = x³ + 5
• Inverse does not exist

Find the inverse of the function including any restriction on domain

• f^-1 = (x + 3)² − 4, x ≥ −3
• f^-1 = (x − 4)² + 3,  x ≥ 4
• f^-1 = (x + 3)² − 4
• Inverse does not exist

Find the inverse of the function including any restriction on domain

• f^-1 = (x² + 2),  x ≤ 0
• f^-1 = (x² + 1) / 2,  x ≤ 0
• f^-1 = (x² − 1) / 2,  x ≥ 0
• Inverse does not exist

What is the inverse of the function?

What is the inverse of the given function?

Verify if $f\left(x\right)$  and  $g\left(x\right)$  are inverses of each other.

 $f\left(x\right)=4+\frac{1}{3}x$  

 $g\left(x\right)=3x-12$  

SHOW YOUR WORK

• Inverse Functions

• Not Inverse Functions