SOLUTION: given: f(x)= x^2+2 and g(x)= 3x+1 a) find the composition (f of g)(x) b) find the inverse function g^-1(x)

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Question 84674: given: f(x)= x^2+2 and g(x)= 3x+1
a) find the composition (f of g)(x)
b) find the inverse function g^-1(x)
Answer by dolly(163) About Me  (Show Source):
You can put this solution on YOUR website!
f(g(x)) = f(3x+1)
= (3x+1)^2 +2
= 9x^2 + 6x + 1 + 2
= 9x^2 + 6x + 3
= 3(3x^2 + 2x + 1)

b) let y = 3x + 1
Interchange x and y
x = 3y + 1
x - 1 = 3y
(x-1)/3 = y
So g^-1 (x) = (x-1)/3