Function Inverses and Evaluations

The video tutorial covers various mathematical concepts including evaluating functions, finding inverse functions, solving equations, and analyzing graphs. It explains how to calculate the value of a function at a given point, find the inverse of a function, solve for variables, and verify if functions are inverses. Additionally, it discusses how to determine if a graph represents a function and identify one-to-one functions using the horizontal line test. The tutorial concludes with finding the domain of a function division.

What is the value of f(2) for the function given in the video?

• 21

• 15

• 23

• 19

What is the inverse function of the given function?

• (x^5 - 3)/7

• (x^3 + 5)/7

• (x^3 - 5)/7

• (x^5 + 3)/7

If f(x) = -15, what is the value of x?

• 4

• -4

• 3/2

• -3/2

What is f(g(x)) if g(x) = x - 5?

• x^2 - 3x + 8

• x^2 - x + 6

• x^2 - 5x + 10

• x^2 - 7x + 12

What is the value of g(f(2))?

• 4

• 5

• 6

• 7

How can you prove that two functions are inverses of each other?

• By showing f(x) = g(x)

• By showing f(x) = -g(x)

• By showing f(g(x)) = g(f(x))

• By showing f(g(x)) = x and g(f(x)) = x

Which graph does not represent a function?

• Graph D

• Graph C

• Graph B

• Graph A

Which graph is not a one-to-one function?

• Graph A

• Graph B

• Graph D

• Graph C

If f(4, y) = 48, what is the value of y?

• 8

• 4

• 2

• -8

What is the domain of f/g?

• All real numbers except -3 and 5

• All real numbers except -2 and 4

• All real numbers except -5 and 3

• All real numbers except -4 and 2