Answer:
1. g(f(-2)) = -19
2. f(f(-1)) = -1
Explanation:
1. g(f(-2)) where f(x) = 5x + 2 and g(x) = 2x-3
you're on the right track! g(f(x)) means that g's x is equal to the function f, in which you would plug in the answer for f (or equation in some cases) and that would be the x term of g. g(f(x)) or (g°f) can be said as "g composed of f"
what i would do first to make it a bit more simpler is plug in -2 in f(x) and then plug in that answer into g(f(x))
f(-2) = 5(-2) + 2 = -10 + 2 = -8
f(-2) = -8
in your steps, you put g(-2) = -8, when it is f(-2) = -8,
what you would do after that is plug in -8 into g(f(x))
g(f(-8)) = g(-8) <-- plug in -8 for x in g(x)
g(-8) = 2(-8) - 3 <-- distribute 2 into -8
-16 - 3 = -19
so g(f(-2)) = -19
2. find f(f(-1)) when f(x) = 8 - x
first you want to solve f(-1)
f(-1) = 8 - (-1) = 9
so f(-1) = 9
again, what you did in this composition is solved for the first function (the inside f), but never plugged in the result into the second function
now we want to plug in the answer 9 into f(x)
f(9) = 8 - (9) = -1
so f(9) = -1
this leaves us with the answer: f(f(-1)) = -1