Find (f o g)(7) and (g o f)(7).
f(x)=3x-1; g(x)=x^2+3
(f o g)(x) = f(g(x))
= f(x^2+3)
= 3(x^2 + 3) - 1
(f o g)(7) = 3(49+3) - 1 = 155
(g o f)(x) = g(f(x))
= g(f(x))
= g(3x-1)
= (3x-1)^2 + 3
(g o f)(7)
= (20)^2 + 3 = 403
we could have done these without finding the general function.
I will do the 2nd one that way, you do the 1st the same way.
f(7) = 20
(g o f)(7)
g(f(7))
= g(20) = 20^2 + 3 = 403