SOLUTION: Given: f(x)= 5x^2-7x+3 and g(x)= 4x+9; Find: a. (fog)(x) b. (gof)(x) c. Find functions f and g such that f{g(x)}=h(x); h(x)=(2x+3)^2

Algebra ->  Graphs -> SOLUTION: Given: f(x)= 5x^2-7x+3 and g(x)= 4x+9; Find: a. (fog)(x) b. (gof)(x) c. Find functions f and g such that f{g(x)}=h(x); h(x)=(2x+3)^2      Log On


   

Question 1043660: Given: f(x)= 5x^2-7x+3 and g(x)= 4x+9;
Find:
a. (fog)(x)
b. (gof)(x)
c. Find functions f and g such that f{g(x)}=h(x); h(x)=(2x+3)^2
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
That is better. You are dealing with the composition of functions. You have f and g given.

f%28g%28x%29%29=5%284x%2B9%29%5E2-7%284x%2B9%29%2B3, which is just using g as the input for f.

...and then simplify.
5%2816x%5E2%2B72x%2B81%29-28x-63%2B3
80x%5E2%2B360x%2B81-28x-60
highlight%2880x%5E2%2B332x%2B21%29



g%28f%28x%29%29=4%285x%5E2-7x%2B3%29%2B9
20x%5E2-28x%2B12%2B9
highlight%2820x%5E2-28x%2B21%29