SOLUTION: If f(x)=2x-1/x+1 and g(x)=x/x-4, then what is (f of g)(x) and the domain of (f of g)(x)?

Algebra ->  Functions -> SOLUTION: If f(x)=2x-1/x+1 and g(x)=x/x-4, then what is (f of g)(x) and the domain of (f of g)(x)?      Log On


   

Question 1198434: If f(x)=2x-1/x+1 and g(x)=x/x-4, then what is (f of g)(x) and the domain of (f of g)(x)?
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
If
f%28x%29=%282x-1%29%2F%28x%2B1%29+
and
g%28x%29=x%2F%28x-4%29
then
(f o g)%28x%29=f%28g%28x%29%29

(f+o g)%28x%29=f%28x%2F%28x-4%29%29

(f+o g)%28x%29=%282%28x%2F%28x-4%29%29-1%29%2F%28x%2F%28x-4%29%2B1%29+

(f o g)%28x%29=%282x%2F%28x-4%29-1%29%2F%28x%2F%28x-4%29%2B1%29+

(f+o+g)%28x%29=%28%28x+%2B+4%29%2F%28x+-+4%29%29%2F%28%282+%28x+-+2%29%29%2F%28x+-+4%29%29+

(f+o g)%28x%29=%28x+%2B+4%29%2F%282+%28x+-+2%29%29+


and the domain of (f+o g)%28x%29:
since denominator cannot be equal to zero, exclude x=2
{ x element R : x%3C%3E2 }