[tex]\begin{gathered} f(x)=x-x^3 \\ g(x)=1+x+\frac{3-3x^3}{3} \end{gathered}[/tex]
To check whether the two function are equal or not, let's simplify g(x).
[tex]\begin{gathered} g(x)=1+x+\frac{3}{3}-\frac{3x^3}{3} \\ g(x)=1+x+1-x^3 \\ g(x)=2+x-x^3 \end{gathered}[/tex]
As we can see, f(x) is not equal to g(x).
[tex]\begin{gathered} f(x)\ne g(x) \\ x-x^3\ne2+x-x^3 \end{gathered}[/tex]
For example, at x = 2.
[tex]\begin{gathered} f(x)=x-x^3 \\ f(2)=2-2^3 \\ f(2)=2-8 \\ f(2)=-6 \end{gathered}[/tex][tex]\begin{gathered} g(x)=2+x-x^3 \\ g(2)=2+2-2^3 \\ g(2)=2+2-8 \\ g(2)=-4 \end{gathered}[/tex]
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.
