Question

Let f(x) = x + 2 and g(x) = 2x^2. Perform the function operation, (f.g)(x),and then find the domain of the result. (^2 means raised to the power of 2,or it is an exponent.)

Answer 1

Given the function f(x) and g(x) defined as follows:

`\begin{gathered} f(x)=x+2 \\ g(x)=2x^2 \end{gathered}`
`\begin{gathered} (f\mathrm{}g)(x)=f(x)\cdot g(x) \\ =2x^2(x+2) \\ (f\cdot g)(x)=2x^3+4x^2 \end{gathered}`

The domain of a function is the set of all possible values of x.

Since x can take on any value in (f.g)(x), we say the domain of the function is the set of real numbers, R.