Exploring Inverse Functions

This video tutorial covers inverse functions, explaining how they reverse the effect of another function. It details methods to find inverses, including algebraic manipulation and composite functions. The tutorial provides step-by-step instructions for solving equations to find inverses and demonstrates how to verify inverses using composite functions.

What is the primary action that an inverse function performs?

• It squares the output of the original function.

• It reduces the output of the original function to zero.

• It multiplies the output of the original function.

• It undoes the action of another function.

What is the first step in finding the inverse of a function algebraically?

• Graph the function to check its symmetry.

• Replace f(x) with y in the equation.

• Solve for y in the equation.

• Switch the x's and y's in the equation.

After switching x and y in the function equation, what is the next step?

• Solve for y.

• Check for line symmetry.

• Graph the function.

• Substitute back into the original function.

How do you solve for y when the equation is x = 3y^2 + 8?

• Subtract 8, divide by 3, and take the square root.

• Divide by 3 and take the square root.

• Add 8 and multiply by 3.

• Subtract 8 and divide by 3.

What is the correct inverse function notation for f(x)?

• 1/f(x)

• f(x+1)

• f^-1(x)

• f(x)^-1

In evaluating composite functions, what is the first function you look at?

• The simplest function.

• The most complex function.

• The inner function.

• The outer function.

What is the result of g(f(2)) if f(2) = 17 and g(x) = x + 3?

• 14

• 20

• 17

• 23

If f(g(x)) = x and g(f(x)) = x, what can be said about f and g?

• They are unrelated functions.

• They are identical functions.

• They are inverse functions.

• They are composite functions.

What happens when you evaluate f(g(x)) where f(x) = x + 5 and g(x) = x - 5?

• Results in x

• Results in x^2

• Results in 0

• Results in 1

How do you verify if two functions are inverses using composite functions?

• Check if f(g(x)) = g(f(x)) = 1

• Check if f(g(x)) = g(f(x)) = 0

• Check if f(g(x)) = g(f(x)) = x

• Check if f(g(x)) = g(f(x)) = x^2