Question

Let f(x) = x + 1 and G(x)=1/x What is the range of (F*G)(X)

Answer 1

`</p><p>f(x)=x+1 \\</p><p>g(x)=(1)/(x) \\</p><p>(f\cdot g)(x)=(x+1)(1)/(x) \\</p><p>(f\cdot g)(x)=\underline{(x+1)/(x)} \\ \\</p><p>0=(x+1)/(x) \\</p><p>0=(x)/(x)+(1)/(x) \\</p><p>0=1+(1)/(x) \\</p><p>-1=(1)/(x) \\</p><p>-x=1 \\</p><p>x=1 </p><p>`

Answer 2

`y \\e1`

Step-by-step explanation

The given functions are

`f(x) = x + 1`

and

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

We want to find

`(f * g)(x)`

We use function properties to obtain:

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

`(f * g)(x) = (x + 1) * (1)/(x) = (x + 1)/(x)`

There is a horizontal asymptote at:

`y = 1`

Let

`y = (x + 1)/(x)`

`xy = x + 1`

`xy - x = 1`

`x(y - 1) = 1`

`x = (1)/(y - 1)`

The range is

`y \\e1`

Or

`( - \infty ,1) \cup(1, \infty )`