SOLUTION: Thank you in advance for helping me with this problem. I need to find the (f o g)x and (g o f)x and the domain for each. f(x)=2x^2-x-1, g(x)=x+4

Algebra ->  Functions -> SOLUTION: Thank you in advance for helping me with this problem. I need to find the (f o g)x and (g o f)x and the domain for each. f(x)=2x^2-x-1, g(x)=x+4      Log On


   

Question 176358This question is from textbook college algebras
: Thank you in advance for helping me with this problem. I need to find the
(f o g)x and (g o f)x and the domain for each.
f(x)=2x^2-x-1, g(x)=x+4 This question is from textbook college algebras

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
f%28x%29=2x%5E2-x-1
g%28x%29=x%2B4
.
.
.
There are no restrictions on the domain of either functions. All values are defined for f(x) and g(x). The domains are therefore,
(-infinity,infinity)
.
.
.
f%28g%28x%29%29=2%28x%2B4%29%5E2-%28x%2B4%29-1
f%28g%28x%29%29=2%28x%5E2%2B8x%2B16%29-x-4-1
f%28g%28x%29%29=2x%5E2%2B16x%2B32-x-5
f%28g%28x%29%29=2x%5E2%2B15x%2B27
.
.
No restrictions on the domain of f(g(x)),
(-infinity,infinity)
.
.
.
g%28f%28x%29%29=%282x%5E2-x-1%29%2B4
g%28f%28x%29%29=2x%5E2-x%2B3
.
.
No restrictions on the domain of g(f(x)),
(-infinity,infinity)