Inverse Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect 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 and g are inverse functions, what is true about f(g(x))?

Back

f(g(x)) = x for all x in the domain of g.

Front

If f(2) = -1, what is g(-1)?

Back

g(-1) = 2, since f and g are inverse functions.

Front

What is the inverse of the function f(x) = 2x + 3?

Back

f⁻¹(x) = (x - 3)/2.

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f⁻¹(x).

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across the line y = x.

Front

If f(x) = x², what is the inverse function?

Back

f⁻¹(x) = √x, but only for x ≥ 0, since f(x) is not one-to-one over all real numbers.

Front

What does it mean for two functions to be inverses?

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in their respective domains.

Front

What is the inverse of the points (1, 2), (3, 4)?

Back

The inverse points are (2, 1), (4, 3).

Front

If g(1) = -2, what is f(-2)?

Back

f(-2) = 1, since f and g are inverse functions.