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.
