Composition of 3 functions

[nickmx50]

Here's the problem f(x) = X^2-3x+5 g(x)= sin^2(3-x) h(x)=e^(x-3)

find h(f(g(x)))

I started by finding f(g(x)) or f(sin^2(3-x)) which comes out (sin^2(3-x))^2 - 3(sin^2(3-x)) + 5

from there I'm not sure what indentity to use. My TI-89 simplifies that to (2-(sin^2(x-3))(cos^2(x-3))+3

Then it simplifies it to cos^4(x-3) + cos^2(x-3) + 3

If that would plug into h(X) then you would get an answer of e^(cos^4(x-3) + cos^2(X-3))

I'm just not seeing the steps to get there. Appreciate the help. Thanks

 

[mmm4444bot]

Here's the problem f(x) = X^2-3x+5 g(x)= sin^2(3-x) h(x)=e^(x-3)

find h(f(g(x))) …

… My TI-89 simplifies that to (2-(sin^2(x-3))(cos^2(x-3))+3 …

Your TI-89 output 5 open parentheses and 4 close parentheses. :?

Are you instructed to simplify the composed expression for h(f(g(x))) ?

 

[nickmx50]

Oh sorry about the parentheses mistake. I figured it out using the pythagorean identity, sin^2(x) + cos^2(x) = 1. Thanks