Inverses of Linear Functions

Front

What is the inverse of the function f(x) = -4x - 12?

Back

f^-1(x) = -1/4x - 3

Tags

CCSS.HSF-BF.B.4A

Front

What line do inverses of functions reflect over?

Back

y = x

Tags

CCSS.HSF-BF.B.4C

Front

What is the general form of the inverse of a linear function?

Back

If f(x) = mx + b, then f^-1(x) = (x - b)/m.

Tags

CCSS.HSF-BF.B.4A

Front

How do you find the inverse of a function algebraically?

Back

1. Replace f(x) with y. 2. Swap x and y. 3. Solve for y. 4. Replace y with f^-1(x).

Tags

CCSS.HSF-BF.B.4A

Front

What is the significance of the slope in the inverse of a linear function?

Back

The slope of the inverse is the reciprocal of the original function's slope.

Tags

CCSS.HSF-BF.B.4C

Front

If f(x) = 2x + 5, what is f^-1(x)?

Back

f^-1(x) = (x - 5)/2.

Tags

CCSS.HSF-BF.B.4A

Front

What does it mean for two functions to be inverses of each other?

Back

f(f^-1(x)) = x and f^-1(f(x)) = x for all x in the domain.

Tags

CCSS.HSF-BF.B.4B

Front

What is the domain of the inverse function if the original function is f(x) = -4x - 12?

Back

The domain of the inverse is the range of the original function.

Tags

CCSS.HSF-BF.B.4C

Front

What is the range of the inverse function if the original function is f(x) = -4x - 12?

Back

The range of the inverse is the domain of the original function.

Front

How can you verify that two functions are inverses?

Back

By showing that f(f^-1(x)) = x and f^-1(f(x)) = x.

Tags

CCSS.HSF-BF.B.4B