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, replace f(x) with y, swap x and y, and then solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

What is the inverse of f(x) = 2x + 3?

Back

f⁻¹(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

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.

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

How do you verify if two functions are inverses?

Back

To verify, check if 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 f(x) = 3x - 5?

Back

f⁻¹(x) = (x + 5)/3.

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

Front

If f(x) = 5x + 2, what is f⁻¹(10)?

Back

f⁻¹(10) = (10 - 2)/5 = 1.6.

Tags

CCSS.HSF-BF.B.4A