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

How do you find the inverse of a function algebraically?

Back

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

Front

What is the composition of functions?

Back

The composition of functions f and g, denoted as f(g(x)), means applying g first and then applying f to the result.

Front

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

Back

Two functions f and g are inverses if f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Front

What is the graphical representation of inverse functions?

Back

The graph of an inverse function is a reflection of the original function across the line y = x.

Front

How do you verify if two functions are inverses?

Back

To verify, compute f(g(x)) and g(f(x)). If both equal x, then they are inverses.

Front

What is the inverse of f(x) = x² for x ≥ 0?

Back

f⁻¹(x) = √x.

Front

If f(x) = 5x - 2, what is f⁻¹(x)?

Back

f⁻¹(x) = (x + 2)/5.

Front

What is the inverse of f(x) = 1/x?

Back

f⁻¹(x) = 1/x.