Question

Suppose that the functions g and h are defined for all real numbers x as follows. g(x) = 2x+2, h(x) = 5x. Write the expressions for (g-h)(x) and (g x h)(x) and evaluate (g+h)(-1).

Answer 1

Answer:
`(g-h)(x) =-3x+2`

`(g* h)(x)=10x^2+10x`

`(g+h)(-1)=-5` .

Explanation:

Given,
`g(x) = 2x+2\\ h(x)=5x`

To write: the expressions for
`(g-h)(x)` and
`(g x h)(x)` .

To evaluate :
`(g+h)(-1).`

As
`(g-h)(x) = g(x)-h(x)`

`= (2x+2-(5x))` [substituting the values of
`g(x)` and
`h(x)`]

`= 2x-5x+2=-3x+2`

So,
`(g-h)(x) =-3x+2`

Now,
`(g * h)(x)= g(x)* h(x) =(2x+2)* 5x`

`=2x* 5x +2*5x\\=10x^2+10x\\\\\Rightarrow\ (g* h)(x)=10x^2+10x`

Now,
`(g+h)(-1)= g(-1)+h(-1) = (2(-1)+2)+(5(-1))=-2+2-5=-5`

So,
`(g+h)(-1)=-5` .