Question 227039
Find (f &#9702; g)(1), (g &#9702; f)(1), (f &#9702; g)(x), and (g &#9702; f)(x) where f(x) = 3x^2 + 4 and g(x) = 4x – 1<br>

well first we find (f &#9702; g)(x).  To do this we plug in g(x) every time we find an x in f(x).<br>

(f &#9702; g)(x) = 3(4x-1)^2+4.<br>

Now we just simplify.  I will leave this up to you but you should end up with 48x^2-24x+7.<br>

Now we find (g &#9702; f)(x).  To do this we plug in f(x) every time we find an x in g(x).<br>

(g &#9702; f)(x) = 4(3x^2+4) - 1<br>

Now we just simplify.  Again I will leave this for you to do but you should end up with 12x^2+15.<br>

Next we Find (f &#9702; g)(1).  To do this we plug 1 in for x.  <br>

(f &#9702; g)(1) = 48(1)^2-24(1)+7 = 48-24+7 = 31<br>

Last we find (g &#9702; f)(1).  To do this we plug 1 in for x.<br>

(g &#9702; f)(1) = 12(1)^2+15 = 12+15 = 27<br>