Question

The domain of both

f(x)=x−6
and








g(x)=x+6
is all real numbers. What is the domain of














h(x)=f(x)g(x)
?

Answer 1

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

Domain: (-∞,∞)

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 (-∞,∞)