find fogoh f(x)=5x-7, g(x)=x^2, h(x)=7-x

Question

I have been trying to solve this problem, I keep coming up with 8x^2 +5x +42, can I get help, thanks

Answer 1

fºgºh is the same as saying f(g(h(x))).

 

So start by plugging the result of h into the rule for g:

 

g(x)=x²,so g(h(x)) = (h(x))²

 

So g(h(x)) = (7-x)²

 

Now take f() of that.

 

f(x) = 5x-7 so f(g(h(x))) is 5((7-x)²) - 7

 

That is equal to 5(49 -14x + x²) - 7= 245 - 70x + 5x² - 7 = 238 - 70x + 5x²

 

or...

 

5x² - 70x + 238

 

 

Answer 2

f(x) = 5x - 7

g(x) = x²

h(x) = 7 - x

 

g o h(x) = (7 - x)²

f o g o h = 5(7 - x)² - 7

f o g o h = 5(49 - 14x + x²) - 7

f o g o h = 5x² - 70x + 245 - 7

f o g o h = 5x² - 70x + 238