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 f^-1(y) will take 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 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

What is the relationship between a function and its inverse?

Back

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

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 the domain.

Front

If f^-1(-25) = 7, what is f(7)?

Back

f(7) = -25.

Front

How can you verify if two functions are inverses?

Back

To verify if two functions are inverses, check if f(g(x)) = x and g(f(x)) = x.

Front

What is the inverse of a quadratic function?

Back

The inverse of a quadratic function is not a function unless it is restricted to a domain where it is one-to-one.

Front

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

Back

The inverse function is f^-1(x) = √x, but only for x ≥ 0.