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

If we are going to multiply the expression for f(x) and that for g(x), we will get,

                        (x + 7)(1/x-13)

This can be further simplified into,

                        (x + 7)(x – 13)

In this simplified expression, it can be noted that all real numbers can be used to replace x in the expression except for 13. This is because if we replace x with 13, it will make our denominator equal to 0 and our expression becomes indefinite.

The answer is that the domain of (f*g)(x) is all real numbers except 13.

for this pair of functions g(x)=x-2 and f(x)=|x| is (g o f)(a)= |a| -2

step-by-step explanation:

g(x)=x-2

f(x)=|x|

(g o f)(a)=?

(g o f)(x)=g(f(x))

(g o f)(x)=g(|x|)

(g o f)(x)=|x|-2

(g o f)(a)=|a|-2