Understanding Domains of Inverse Functions

This video tutorial explains how to find the domain of inverse functions. It covers linear, quadratic, radical, and rational functions, emphasizing the importance of the horizontal line test for determining if an inverse exists. The tutorial provides step-by-step instructions for finding inverses and discusses domain and range transformations, including handling domain restrictions for quadratic functions and asymptotes for rational functions.

What is the domain of the inverse function for a linear function with no restrictions?

• All real numbers

• Only negative numbers

• Numbers between -1 and 1

• Only positive numbers

Why does a quadratic function need domain restriction to have an inverse?

• It is not differentiable

• It does not pass the vertical line test

• It is not continuous

• It does not pass the horizontal line test

What is the domain of the inverse function for the restricted quadratic function x^2 - 3?

• From -3 to infinity

• From -infinity to 0

• From -infinity to -3

• From 0 to infinity

For a square root function, what must the inside of the radical be?

• Less than zero

• Greater than zero

• Equal to zero

• Greater than or equal to zero

What is the domain of the inverse function for the square root function √(8 - 2x)?

• From -infinity to 0

• From -3 to infinity

• From -infinity to 4

• From 0 to infinity

What is the horizontal asymptote for a rational function where the degrees of the numerator and denominator are equal?

• The sum of the leading coefficients

• Infinity

• Zero

• The ratio of the leading coefficients

Why must the horizontal asymptote be removed from the range of a rational function?

• It is always negative

• It is always positive

• It is always zero

• The graph never touches it

What is the domain of the inverse function for the rational function 3x + 2 / 5x - 4?

• From 3/5 to infinity

• From 4/5 to infinity

• From -infinity to 4/5

• From -infinity to 3/5

What happens when you plug the horizontal asymptote value into the original function?

• You get an undefined result

• You get a valid x value

• You get a negative number

• You get a zero

What is the key to finding the domain of an inverse function?

• Finding the domain of the original function

• Finding the range of the original function

• Finding the x-intercepts

• Finding the y-intercepts