Exploring Inverse Functions and Their Graphs

What is the primary concept behind inverse functions?

• They add a constant to inputs

• They repeat the input as output

• They cancel each other out

• They multiply inputs by a constant

What does it mean for two functions to be inverses of each other?

• They produce the same outputs

• They nullify each other's effects

• They have the same graph

• They are both linear functions

What happens when you apply an inverse function after its original function?

• The number doubles

• The number becomes zero

• You get the original number back

• You get a new random number

What is the result of applying function G after function F on a number in the provided example?

• The original number is halved

• The original number is tripled

• The original number is returned

• The original number is squared

Why is the notation F^-1(x) not considered an exponent?

• Because it indicates subtraction

• Because it denotes a square root

• Because it signifies an inverse function

• Because it represents division

What is the horizontal line test used for?

• To verify if a function has an inverse

• To find the maximum value of a function

• To check if a function is continuous

• To determine if a function is increasing

Why can't the function y = x^2 have an inverse that is also a function?

• It is not a polynomial

• It fails the horizontal line test

• It passes the horizontal line test

• It fails the vertical line test

What does the point (a, b) on the graph of a function imply about its inverse?

• The point (a, b) is also on the inverse

• The point (b, a) is on the inverse

• The point (-a, -b) is on the inverse

• No related point is on the inverse

Which type of function always passes the horizontal line test?

• Quadratic functions

• Exponential functions

• Cubic functions

• Absolute value functions

How can you graphically represent the inverse of a function?

• By reflecting it about the line y = x

• By stretching it horizontally

• By rotating it 90 degrees

• By translating it upwards