COMPOSITE FUNCTION WORKSHEET
For 1- 9: Let f(x) = 2x – 1, g(x) = 3x, and h(x) = x2 + 1.
Compute the following:
1. f(g(-3)) : Work inside-out: g(-3) = -9. Then f(-9) = -19.
4. f(g(h(2))) : h(2) = 2! + 1 = 5. 𝑔 5 =15. f(15) = 29.
7. f( x + 1) : put (x+1) in for x in f(x). So, f(x+1) = 2(x+1)-1.
Distribute: 2x+2-1 = 2x+1.
For 10-11: Let f(x) = -3x + 7 and g(x) = 2x2 – 8. Compute
the following:
10. f(g(x)) : g(x) = 2x2-8. f(2x2-8) = -3(2x2-8)+7 = -6x2+24-7.
This equals -6x2+17. Domain is all reals.
11. (g◦f)(x) = g(f(x)) = g(-3x+7) = 2(-3x+7)2 - 8.
2(9x2-42x+49)-8 = 18x2-84x+98 – 8
=18x2-84x + 90.
12. If f(x) = 3x-5 and g(x) =x2. find f(g(3))
g(3) = 9. f(9) = 3(9)-5 = 27-5 = 22.
17. f(x) = -9x+3 and g(x) = x4. Find f(g(x)).
f(x4) = -9(x4)+3 = -9x4+3. domain is all reals.
19. f(x) = x2+7 and g(x) = x-3. Find f(g(x))
f(x-3) = (x-3)2+7 = x2-6x+9 +7 = x2-6x+16.
21. f(x)=x-1 and g(x) = x2+2x-8. find g(f(x)).
g(x-1) = (x-1)2+2(x-1)-8 = x2-2x+1 +2x -2 -8 =
x2-9.