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

How do you determine if a relation is a function?

Back

A relation is a function if each input (x-value) is associated with exactly one output (y-value).

Front

What is the graphical representation of an inverse function?

Back

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

Front

What is the first step in finding the inverse of a function?

Back

Switch x and y in the equation.

Front

How do you find the inverse of a linear function?

Back

To find the inverse of a linear function, switch x and y, then solve for y.

Front

What is the inverse of f(x) = 3x - 5?

Back

f⁻¹(x) = (x + 5)/3.

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 for all x in the domain, then f and g are inverse functions.

Front

Can a function have more than one inverse?

Back

No, a function can have at most one inverse. If it has more than one, it is not a function.

Front

What is the horizontal line test?

Back

The horizontal line test determines if a function is one-to-one. If any horizontal line intersects the graph more than once, the function does not have an inverse.

Front

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

Back

f⁻¹(x) = √x.