ALG 2 Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x and produces an output y, then the inverse function f⁻¹(y) takes y back to x.

Front

If f(f⁻¹(x)) = x, what does this imply?

Back

This implies that f and f⁻¹ are inverse functions of each other.

Front

What is the notation for an inverse function?

Back

The notation for an inverse function is f⁻¹(x).

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

How do you find the inverse of a function algebraically?

Back

To find the inverse, replace f(x) with y, swap x and y, and then solve for y.

Front

What is the relationship between the graphs of a function and its inverse?

Back

The graphs of a function and its inverse are reflections of each other across the line y = x.

Front

If f(x) = x², is f⁻¹(x) defined for all x?

Back

No, f(x) = x² is not one-to-one, so it does not have an inverse for all x. It can be restricted to x ≥ 0.

Front

What is the value of f(7) if f⁻¹(-25) = 7?

Back

f(7) = -25.

Front

Calculate g(f(-1)) if f(x) = 4x² - 4 and g(x) = -3x + 2.

Back

g(f(-1)) = 2.

Front

What is f(g(3)) if f(x) = x² - 3x and g(x) = 4x + 2?

Back

f(g(3)) = 154.