Mathematics: For f(x) = x+6 and g(x) = 2x + 3, find the following a. (fog)(x) b. (g of)(x) c. (fog)(2)

Boys are better 7/10 people said maybe?Step-by-step explanation:...

For f(x) = x+6 and g(x) = 2x + 3, find the following

lunaangelique1p442id

16.03.2021

(f o g)(x) = 2x + 9

(g o f)(x) = 2x + 15

(f o g)(2) = 11

Step-by-step explanation:

Given

f(x) = x+6

g(x) = 2x + 3

Solving (a): (f o g)(x)

In functions:

(f o g)(x) = f(g(x))

Solving for f(g(x))

f(x) = x+6

f(g(x)) = 2x + 3 + 6

f(g(x)) = 2x + 9

So:

(f o g)(x) = 2x + 9

Solving (a): (g o f)(x)

In functions:

(g o f)(x) = g(f(x))

Solving for g(f(x))

g(x) = 2x + 3

g(f(x)) = 2(x+6)+3

Open bracket

g(f(x)) = 2x+12+3

g(f(x)) = 2x+15

So:

(g o f)(x) = 2x + 15

Solving (c): (f o g)(2)

In (a):

(f o g)(x) = 2x + 9

Substitute 2 for x

(f o g)(2) = 2*2 + 9

(f o g)(2) = 4 + 9

(f o g)(2) = 11

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