Question
Asked Sep 12, 2019
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For the pair of functions

f(x)

and

g(x),

find

f(g(x)),
g(f(x))

and

f(f(x)).
f(x) = x3 − x;  g(x) = 
x4 − 3
x4 + 3
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Expert Answer

Step 1

Given,

...
f (x) x3x
x-3
g(x)
x4+3
Now
)'-
(x+-3
(xt-3Y
x4+3.
f(o)
x4 +3
x4+3
2
x-3
x4 +3,
x4+3,
g(f (x)) = g(x3 - x) = (3-x)4-3
(3-x)4+3
x12-4x10+6x8-4x6+x4-3
x12-4x10+6x8-4x6+x4+3
f(f(x)) f(x-x) = (x3 - x)3- (x3
— х9 — Зх7 + Зx5 — х3 — х3 +x
— х9 — Зх7 + Зx5 — 2х3 + х
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Image Transcriptionclose

f (x) x3x x-3 g(x) x4+3 Now )'- (x+-3 (xt-3Y x4+3. f(o) x4 +3 x4+3 2 x-3 x4 +3, x4+3, g(f (x)) = g(x3 - x) = (3-x)4-3 (3-x)4+3 x12-4x10+6x8-4x6+x4-3 x12-4x10+6x8-4x6+x4+3 f(f(x)) f(x-x) = (x3 - x)3- (x3 — х9 — Зх7 + Зx5 — х3 — х3 +x — х9 — Зх7 + Зx5 — 2х3 + х

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Tagged in

Math

Calculus

Functions