Question

Suppose that the functions f and g are defined for all real numbers x as follows.

f(x) = x - 5, g(x) = 2(x) + 6
Write the expressions for (f*g)(x) and (f-g)(x)..

Answer 1

`(f*g)(x)=2x^(2)-4x-30\\`

`(f-g)(x)=-(x+11)\\`

Explanation:

the expression (f*g)(x) can be expanded as follows

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

since
`f(x)=x-5,g(x)=2x+6`

Hence

`(f*g)(x)=f(x)*g(x)\\(f*g)(x)=(x-5)*(2x+6)\\(f*g)(x)=2x^(2)+6x-10x-30\\(f*g)(x)=2x^(2)-4x-30\\`

also the expansion for (f-g)(x) is express as

`(f-g)(x)=f(x)-g(x)\\`

also since

`f(x)=x-5,g(x)=2x+6` then when we substitute values, we have

`(f-g)(x)=(x-5)-(2x+6)\\(f-g)(x)=x-5-2x-6\\(f-g)(x)=-x-11\\(f-g)(x)=-(x+11)\\`

For this type of operation kindly note the below expansions

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

`(f-g)(x)=f(x)-g(x)\\`

`(f+g)(x)=f(x)+g(x)\\`

`(f/g)(x)=f(x)/g(x)\\`