Inverses - Compositions

Front

What is the definition of 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 find the inverse of a function algebraically?

Back

To find the inverse of a function, replace f(x) with y, swap x and y, and then 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 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

If f(g(x)) = x, what does this imply about f and g?

Back

It implies that g is the inverse of f, and vice versa.

Front

What is the first step in finding f(g(x))?

Back

The first step is to evaluate g(x) and then substitute that result into f.

Front

True or False: The function f(x) = 2x + 3 has an inverse that is also a linear function.

Back

True.

Front

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

Back

The inverse is f^-1(x) = (x + 5)/3.

Front

How do you verify if two functions are inverses of each other?

Back

To verify, show that f(g(x)) = x and g(f(x)) = x for all x in the domain.

Front

What is the inverse of the function g(x) = (x - 9)/3?

Back

The inverse is g^-1(x) = 3x + 9.