To find the product of the functions [tex]\( f(x) = x + 3 \)[/tex] and [tex]\( g(x) = x - 3 \)[/tex], we need to multiply these two functions together.
Let's define the product of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex] as [tex]\( h(x) \)[/tex].
So, [tex]\( h(x) = f(x) \cdot g(x) \)[/tex].
Substitute the expressions for [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex]:
[tex]\[ h(x) = (x + 3) \cdot (x - 3) \][/tex]
Using the difference of squares formula [tex]\( (a + b)(a - b) = a^2 - b^2 \)[/tex]:
[tex]\[ h(x) = x^2 - 3^2 \][/tex]
Simplify the expression:
[tex]\[ h(x) = x^2 - 9 \][/tex]
Now let's evaluate [tex]\( h(x) \)[/tex] at a specific value of [tex]\( x \)[/tex]. For instance, let’s choose [tex]\( x = 1 \)[/tex]:
[tex]\[ h(1) = 1^2 - 9 \][/tex]
Calculate the value:
[tex]\[ h(1) = 1 - 9 \][/tex]
[tex]\[ h(1) = -8 \][/tex]
Thus, the product of the functions [tex]\( f(x) = x + 3 \)[/tex] and [tex]\( g(x) = x - 3 \)[/tex] evaluated at [tex]\( x = 1 \)[/tex] is:
[tex]\[ h(1) = -8 \][/tex]
