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 :

JeanaShupp

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] .

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