The product of two functions f(x)*g(y), when f(x) = tan(x)-2/x and g(x) = x^2+8 is,
[tex]f(x)\times g(y)= y^2\tan(x)+8\tan(x)-\dfrac{2y^2}{x}-\dfrac{16}{x}[/tex]
What is the product of functions?
When the two or more than two functions are multiplies together. Then the resultant function is called the product of these functions.
Let suppose there is a function f(x) and another function g(x). Then the product of function can be written as,
[tex]f(x)\times g(x)[/tex]
Let suppose, a function f(x) is
[tex]f(x)= tan(x)-\dfrac{2}{x}[/tex]
Let another function g(x) is,
[tex]g(x)= x^2+8[/tex]
Then g(y), will be,
[tex]g(y)= y^2+8[/tex]
The product of this two function is,
[tex]f(x)\times g(y)= \left(\tan(x)-\dfrac{2}{x}\right)\times(y^2+8)\\f(x)\times g(y)= y^2\tan(x)+8\tan(x)-\dfrac{2y^2}{x}-\dfrac{16}{x}[/tex]
Thus, the product of two functions f(x)*g(y), when f(x) = tan(x)-2/x and g(x) = x^2+8 is,
[tex]f(x)\times g(y)= y^2\tan(x)+8\tan(x)-\dfrac{2y^2}{x}-\dfrac{16}{x}[/tex]
Learn more about the composite function here;
https://brainly.com/question/10687170
