Any ideas?
The fractions are throwing me off plus there is an x on top of one of them.
Given f(x)=5x/x-4 and g(x)=6/x+2 find the following
a) (f+g)(x)
b) the domain of (f+g)(x) in interval notation
c) (f-g)(x)
d) the domain of (f-g)(x) in interval notion
e) (f*g)(x)
f) the domain of (f*g)(x)
g) (f/g)(x)
h. the domain of (f/g)(x) in interval notation
2 answers
Really? By precalc, fractions should not be troubling you. And don't be afraid of using parentheses to make sure your expressions are correct.
(f+g)(x) = f(x) + g(x) = 5x/(x-4) + 6/(x+2) = (5x^2+16x-24) / ((x+2)(x-4))
since division by zero is undefined, the domain is (-∞,-2)U(4,∞)
Now try the others. Since the original domains exclude -2 and 4, the composite domain will also, even if its simplified form allows them.
(f+g)(x) = f(x) + g(x) = 5x/(x-4) + 6/(x+2) = (5x^2+16x-24) / ((x+2)(x-4))
since division by zero is undefined, the domain is (-∞,-2)U(4,∞)
Now try the others. Since the original domains exclude -2 and 4, the composite domain will also, even if its simplified form allows them.