Finding Nonlinear Inverses with Domain Restrictions

Match the following domain restrictions of the inverse given the square root function.

Choose all that are correct. Which statements about inverses are correct?

• The inverse of a square root is a quadratic with a domain restriction.

What is the inverse function of a quadratic (x²)?

• A square root function

• 2x

• Another quadratic

• A linear function

Mathematical Equivalence

ON

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

Mathematical Equivalence

ON

Which equation below must have a restricted domain, in order to find the inverse function?

Find the inverse of the function including any restriction on the domain.

• f^-1 = x³ − 5, x ≥ 5

• f^-1 = x³ + 5,  x ≥ 0

• f^-1 = x³ + 5

• Inverse does not exist

Restricting the domain is another way to say restricting the...

• y-values

• x-values

• Odd numbers

• Even numbers