Given f(x) = 3x + 2 and g(x) = -2x2+4 Find f(g(2))

Question

Given f(x) = 3x + 2 and g(x) = -2x²+4

Find f(g(2))

What would you do in order to solve? Explain in words the process to solving f(g(2)).

Answer 1

f(x) = 3x +2

g(x) = -2x^2 +4

g(2) = -2(2^2) +4 = -8+4=-4

f(g(2)) = f(-4) = 3(-4)+2 =-12+2 =-10

f(g(2)) = -10

or work the problem another way

f(g(x)) = 3(-2x^2 +4) +2

= -6x^2 +12 +2

= -6x^2 +14

f(g(2)) = -6(2)^2 +14 = -24+14 = -10

get the same answer working the problem with 2 different methods, and odds are very good it's correct

Answer 2

Start on the inside of f(g(2)) and determine what g(2) is. To know that, take the function g(x) = -2x² + 4 and plug in x = 2:

g(2) = -2(2)² + 4 = -2(4) + 4 = -8 + 4 = -4

Then take the -4 you got and plug it into f(x):

f(-4) = 3(-4) + 2 = -12 + 2 = -10

So f(g(2)) = -10