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Find f(g(x)) and g(f(x)).
Given: f(x)= 3x – 1; g(x) = 7x + 6

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Answer:

When f(x)= 3x – 1 and g(x) = 7x + 6,

f(g(x)) = 21x + 17

and

g(f(x)) = 21x - 1

Step-by-step explanation:

Given:

f(x) = 3x - 1

g(x) = 7x + 6

To find f(g(x)), substitute the value of g(x) into f(x).

f(g(x)) = f(7x + 6)

Substitute variable.

f(7x + 6) = 3(7x + 6) - 1

Distribute the 3 inside the parenthesis.

f(7x + 6) = 21x + 18 - 1

Subtract 1 from 18.

f(7x + 6) = 21x + 17

Therefore, f(g(x)) is 21x + 17.

To find g(f(x)), substitute the value of f(x) into g(x).

g(f(x)) = g(3x - 1)

Substitute variable.

g(3x - 1) = 7(3x - 1) + 6

Distribute the 7 inside the parenthesis.

g(3x - 1) = 21x - 7 + 6

Add 6 to -7.

g(3x - 1) = 21x - 1

Therefore, g(f(x)) is 21x - 1.

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