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: $(g-h)(x) =-3x+2$

$(g\times h)(x)=10x^2+10x$

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

Step-by-step 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, $(g \times h)(x)= g(x)\times h(x) =(2x+2)\times 5x$

$=2x\times 5x +2\times5x\\=10x^2+10x\\\\\Rightarrow\ (g\times h)(x)=10x^2+10x$

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

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