Answer:
The domain of function [tex]h(x)[/tex] is set of all real numbers.
Domain: (-∞,∞)
Step-by-step explanation:
Given:
[tex]f(x)=x-6[/tex]
[tex]g(x)=x+6[/tex]
the domain of both the above functions is all real number.
To find domain of :
[tex]h(x)=f(x)g(x)[/tex]
Substituting functions [tex]f(x)[/tex] and [tex]g(x)[/tex] to find [tex]h(x)[/tex]
[tex]h(x)=(x-6)(x+6)[/tex]
The product can be written as difference of squares. [tex][a^2-b^2=(a+b)(a-b)][/tex]
∴ [tex]h(x)=x^2-36[/tex]
The degree of the function [tex]h(x)[/tex] is 2 as the exponent of leading term [tex]x^2[/tex] is 2. Thus its a quadratic equation.
For any quadratic equation the domain is set of all real numbers.
So Domain of [tex]h(x)[/tex] is (-∞,∞)
