IM Unit 4 Lessons 15-17 Inverse Functions (Maguire)

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) = y, then the inverse function f⁻¹(y) = x.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, swap the x and y in the equation and solve for y.

Front

If f(x) = 2x + 3, what is the inverse function?

Back

f⁻¹(x) = (x - 3) / 2.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) of a function.

Front

If y = x + 5, what is the inverse?

Back

x = y - 5.

Front

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

Back

If f(g(x)) = x and g(f(x)) = x, then f and g are inverse functions.

Front

If a function gives the amount of water in a tank as a function of time, what does the inverse give?

Back

The inverse gives the time as a function of the amount of water.

Front

If G = 3h, what is the inverse?

Back

h = G / 3.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x-values) for a function.

Front

How do you verify if two functions are inverses?

Back

To verify, check if f(g(x)) = x and g(f(x)) = x for all x in the domain.