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.

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF-BF.A.1C

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.

Tags

CCSS.HSF-BF.B.4C

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.

Tags

CCSS.HSF-BF.B.4B

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.

Tags

CCSS.HSF-BF.A.1C

Front

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

Back

True.

Tags

CCSS.HSF-BF.B.4C

Front

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

Back

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

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF-BF.B.4B

Front

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

Back

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

Tags

CCSS.HSF-BF.B.4A