Question

If f(x)=2x and g(x)= 1/x, what is the domain of (f*g) (x)

Answer 1

The domain of (f*g) (x) is the set of all real numbers; ( -∞, ∞)

Explanation:

(f*g) (x) simply means we obtain the product of f(x) and g(x). We are given that;

f(x)=2x

g(x)= 1/x

(f*g) (x) = f(x) * g(x)

(f*g) (x) = 2x * 1/x = 2

This is a horizontal line defined everywhere on the real line. The domain of (f*g) (x) is thus ( -∞, ∞)

Answer 2

All real numbers

Explanation:

Given :
`f(x)=2x`

`g(x)= (1)/(x)`

To Find : the domain of (f*g) (x)

`f(x)=2x`

`g(x)= (1)/(x)`

`(f\cdot g)(x)=2x * (1)/(x)`

`(f\cdot g)(x)=2`

Since the value of
`(f\cdot g)(x)=2`

So, the domain of the function is
`(f\cdot g)(x)` is all real numbers .