Question

If F(x)=x+7 and G(x)=1/x-13 what is the domain of (f*g)(x)?

Answer 1

The domain of this function is all real numbers such that x does not equal 13.

You can find this by first building the composite function. A composite function is one in which you take the whole function listed second (in this case the g function) and input it for the x in the first function. In some cases simplification may be needed, although it is not here.

f(x) = x + 7

f(g(x)) = $\frac{1}{x - 13} + 7$

Now, to find the domain we have to know what numbers could go in for x. The answer is that we could stick anything in for x, with the exception of 13. Putting 13 into the equation would make the denominator 0, and we cannot divide by 0.

Answer 2

When multiplied together you get the answer of (x+7) / (x-13) and the domain of that is (negative infinity, 13) and (13, infinity)