Does anyone understand this? Find [f ○ (g ○ h)](2) if f(x) = 2x - 1, g(x) = 4x, and h(x) = x2+ 1. ??

2 Answers
Apr 3, 2018

color(blue)(39

Explanation:

f@g@h<=>f(g(h(x)))

Working from the inside out.

h(x)=x^2+1 , g(x)=4x

g(h(x))=4(h(x))=4(x^2+1)

f(x)=2x-1

f(g(h(x))=2(g(h(x)))-1=2(4(x^2+1))-1

=2(4x^2+4)-1=8x^2+8-1=color(blue)(8x^2+7)

f(g(h(x)))(2)=8(2)^2+7=color(blue)(39

Apr 4, 2018

For a different approach, see below.

Explanation:

[f@(g@h)] (2) = f([g@h] (2))

= f(g(h(2))

We'll start by finding h of 2.

We have h(x) = x^2+1, so h(2) = 2^2+1=5.

Therefore,

f(g(color(red)(h(2))) = f(g(color(red)(5))).

Now find g(h(2)) which is the same as g of 5,

Since g(x) = 4x, we get g(5)=4(5)=20.

So,

f(g(5)) = f(20).

Finally, we'll find f of 20.

Since f(x) = 2x-1, we finish with

f(20) = 2(20)-1 = 39