Given f(x) = 2x, g(x) = x + 4 and h(x) = x2, evaluate f(g(h(4))).

Question

i need help solving this equation.

Answer 1

h(x) = x²  => h(4) = 16

 

g(x) = x + 4 => g(h(4)) = g(16) = 20

 

f(x) = 2x => f(g(h(4))) = f(20) = 40

 

This also could have been found as follows:

 

g(h(x)) = h(x) + 4 = x² + 4

f(g(h(x))) = 2g(h(x)) = 2*(x² + 4) = 2x² + 8

 

Then f(g(h(4))) = 2*4² + 8 = 2*16 + 8 = 32 + 8 = 40

Answer 2

H(4)= 4^2 =16

g(h(4))=16+4=20

f(g(h(4)))=2(20)=40

Answer 3

The expression f(g(h(4))) means to take h(4) (the inside) and plug that into the function g(x) and then plug that into the function f(x). You work from inside to outside. 

 

h(4) is the function h(x) when x = 4, so h(4) = 4² = 16.

 

Our expression now becomes f(g(16)). Again working from the inside, g(16) is the function g(x) when x = 16, so g(16) = (16 + 4) = 20. Our expression becomes f(20). 

 

Lastly, f(20) is the function f(x) when x = 20. Plugging in x = 20 into f(x), we get 2×20 = 40.

 

Thus, f(g(h(4))) = 40.