Question

The domain of both

Answer 1

Answer:

The domain of function $h(x)$ is set of all real numbers.

Domain: (-∞,∞)

Step-by-step explanation:

Given:

$f(x)=x-6$

$g(x)=x+6$

the domain of both the above functions is all real number.

To find domain of :

$h(x)=f(x)g(x)$

Substituting functions $f(x)$ and $g(x)$ to find $h(x)$

$h(x)=(x-6)(x+6)$

The product can be written as difference of squares. $[a^2-b^2=(a+b)(a-b)]$

∴ $h(x)=x^2-36$

The degree of the function $h(x)$ is 2 as the exponent of leading term $x^2$ is 2. Thus its a quadratic equation.

For any quadratic equation the domain is set of all real numbers.  

So Domain of $h(x)$ is (-∞,∞)