Algebra 1 Common Core Student Edition, Grade 8-9

Use W it h Lesson 5-5

Concept Byte I Inverse o f a

Linear Function

Common Core State Standards

F-BF.B.4a So l v e a n e q u a t i o n o f t h e f o r m f(x) = cf o r

a simple f unct ion f t hat has an inverse and writ e an

expression f or t he inverse.

MP3

Let/ be a function. If there is a n o th e r function th a t pairs b w i t h a w h e n e v e r / p a i r s

a w i t h b, th e n functions are called inverse functions.

You can find the inverse function algebraically.

Ex a m p l e

Find the inverse of the function / (x) = —2 x + 4.

Step 1 Replace fix) with y. Then switch x for y and y fo r jc.

y = —2 x + 4

x = —2 y + 4

Step 2 Solve for y.

x— 4 — —2y

x - 4 = ~ 2y

-2 -2

— + 2 = y

Write f(x) as y.

Switch x and y.

S ubtract 4 fro m each side.

Divide by - 2.

Simplify.

Step 3 Write in function notation, using / 1 to represent the inverse of the

function f

f ~ \ x ) = - h e + 2

f—: :------------------------------------------------------------------------------------------------------------------------------------------------------------------------n
Ex e r c i se s
Find the inverse of each function.
T— 'h ii 3 1 CM

2. fix) = 3x+ 2 3. f i x ) = —2x — 3


3. fix) = \x + l 5. fix) - 4x + 8 6. fix) = -4x


4. f{x) = 2 - 7 x 8- fix) = \x - 4 9- fix) = - \x + 1


5. fix) = 2x+8 11. f{x) = —4 x + 8 12. fix) = — 1 — 2x


6. f{x) — -7 + x 14. fix) = 4x — 5 15. f{x) = fx - 1


7. fix) = x — 1 17. fix) = — 2 — |x 18. f i x ) = ~ \ x + 1

@ 19. Reasoning Why does interchanging th e x an d y m atch th e definition of an inverse function?

C

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