Inverse Linear Functions

Front

What is an inverse function?

Back

An inverse function reverses the effect of the original function. If f(x) takes x to y, then 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, swap x and y in the equation and solve for y.

Tags

CCSS.HSF-BF.B.4A

Front

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

Back

f⁻¹(x) = (x - 3)/2.

Tags

CCSS.HSF-BF.B.4A

Front

Are the functions f(x) = 2x + 3 and g(x) = (x - 3)/2 inverses of each other?

Back

Yes, they are inverses because f(g(x)) = x and g(f(x)) = x.

Tags

CCSS.HSF-BF.B.4B

Front

What is the graphical representation of inverse functions?

Back

The graphs of inverse functions are reflections of each other across the line y = x.

Tags

CCSS.HSF-BF.B.4C

Front

If f(x) = 3x - 5, what is f⁻¹(2)?

Back

f⁻¹(2) = (2 + 5)/3 = 7/3.

Tags

CCSS.HSF-BF.B.4A

Front

What is the inverse of the coordinates (4, 5)?

Back

The inverse is (5, 4).

Tags

CCSS.HSF-BF.B.4C

Front

How can you tell if two functions are inverses by their graphs?

Back

If the graphs intersect the line y = x at all points, they are inverses.

Tags

CCSS.HSF-BF.B.4C

Front

What is the inverse of f(x) = 1/2x + 1?

Back

f⁻¹(x) = 2(x - 1).

Tags

CCSS.HSF-BF.B.4A

Front

What does it mean if two functions are not inverses?

Back

It means that applying one function after the other does not return the original input.

Tags

CCSS.HSF-BF.B.4B