Question

f(x)= 3x-5 and g(x)= 2-x^2 evaluate:

1.(fog)(x)

2.(gog)(-2)

Answer 1

(fog)(x) means you substitute the whole function of g(x) into the f(x),, we can actually rewrite this (fog)(x) as f(g(x)) --- i think this one is clearer.
now let's substitute g(x) to f(x):
(fog)(x) = f(g(x)) = 3x-5 = 3[g(x)] - 5
(fog)(x) = 3(2 - x^2) - 5
(fog)(x) = 6 - 3x^2 - 5
(fog)(x) = -3x^2 + 1

for #2, we do the same,, we substitute g(x) to g(x) then we evaluate the simplified expression at x=-2:
(gog)(x) = g(g(x)) = 2 - (g(x))^2
(gog)(x) = 2 - (2 - x^2)^2
(gog)(-2) = 2 - [2 - (-2)^2]^2
(gog)(-2) = 2 - [2 - 4]^2
(gog)(-2) = 2 - (-2)^2
(gog)(-2) = 2 - 4
(gog)(-2) = -2

hope this helps~ :)

Answer 2

Thanks a bunch

Answer 3

Yes thank you very much!