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.

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, swap the x and y in the equation and 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 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.

Tags

CCSS.HSF-BF.B.4B

Front

If f(x) = 2x + 3, what is f⁻¹(x)?

Back

f⁻¹(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

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.

Tags

CCSS.HSF-BF.B.4C

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.

Tags

CCSS.HSF-BF.B.4B

Front

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

Back

f⁻¹(x) = √x.

Tags

CCSS.HSF-BF.B.4D

Front

If f(x) = 5x - 2, what is f⁻¹(x)?

Back

f⁻¹(x) = (x + 2)/5.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

f⁻¹(x) = 1/x.

Tags

CCSS.HSF-BF.B.4A