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

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Answer 1 · 2018-04-03T17:49:51

#color(blue)(39#

#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#

Answer 2 · 2018-04-04T13:30:47

For a different approach, see below.

#[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#