Question

Need help on these, thank you!

Answer 1

Answer:

$5x+2 , 2x^2+5x-2,\frac{x^2+5x}{2-x^2}$

Step-by-step explanation:

We are given f(x) and g(x)

1. (f+g)(x)

(f+g)(x) = f(x) + g(x)

           = $x^2+5x+2-x^2$

           = $5x+2$

Domain : All real numbers as it there exists a value of (f+g)(x) f every x .

2. (f-g)(x)

(f-g)(x) = f(x)-g(x)

          = $x^2+5x-2+x^2$

          =$2x^2+5x-2$

Domain : All real numbers as it there exists a value of (f-g)(x) f every x .

Part 3 .

$(\frac{f}{g})(x)\\(\frac{f}{g})(x) = \frac{f(x)}{g(x)}\\=\frac{x^2+5x}{2-x^2}$

Domain : In this case we see that the function is not defined for values of x for which the denominator becomes 0 or less than zero . Hence only those values of x are defined for which

$2-x^2>0$

or $2>x^2$

   Hence taking square roots on both sides and solving inequality we get.

$-\sqrt{2}$