Answer :
Answer: [tex](g-h)(x) =-3x+2[/tex]
[tex](g\times h)(x)=10x^2+10x[/tex]
[tex](g+h)(-1)=-5[/tex] .
Step-by-step explanation:
Given, [tex]g(x) = 2x+2\\ h(x)=5x[/tex]
To write: the expressions for [tex](g-h)(x)[/tex] and [tex](g x h)(x)[/tex] .
To evaluate : [tex](g+h)(-1).[/tex]
As [tex](g-h)(x) = g(x)-h(x)[/tex]
[tex]= (2x+2-(5x))[/tex] [substituting the values of [tex]g(x)[/tex] and [tex]h(x)[/tex]]
[tex]= 2x-5x+2=-3x+2[/tex]
So, [tex](g-h)(x) =-3x+2[/tex]
Now, [tex](g \times h)(x)= g(x)\times h(x) =(2x+2)\times 5x[/tex]
[tex]=2x\times 5x +2\times5x\\=10x^2+10x\\\\\Rightarrow\ (g\times h)(x)=10x^2+10x[/tex]
Now, [tex](g+h)(-1)= g(-1)+h(-1) = (2(-1)+2)+(5(-1))=-2+2-5=-5[/tex]
So, [tex](g+h)(-1)=-5[/tex] .