Question

F(x) = x - x³ andg(x) = 1 + x + (3 - 3x³)/3, each on the domain given by the domain convention.

Answer 1

`\begin{gathered} f(x)=x-x^3 \\ g(x)=1+x+(3-3x^3)/(3) \end{gathered}`

To check whether the two function are equal or not, let's simplify g(x).

`\begin{gathered} g(x)=1+x+(3)/(3)-(3x^3)/(3) \\ g(x)=1+x+1-x^3 \\ g(x)=2+x-x^3 \end{gathered}`

As we can see, f(x) is not equal to g(x).

`\begin{gathered} f(x)\\e g(x) \\ x-x^3\\e2+x-x^3 \end{gathered}`

For example, at x = 2.

`\begin{gathered} f(x)=x-x^3 \\ f(2)=2-2^3 \\ f(2)=2-8 \\ f(2)=-6 \end{gathered}`
`\begin{gathered} g(x)=2+x-x^3 \\ g(2)=2+2-2^3 \\ g(2)=2+2-8 \\ g(2)=-4 \end{gathered}`

At x = 2, the values of f(x) and g(x) are not equal. Hence, the two functions f(x) and g(x) are not equal.