Question

Suppose that the function g is defined, for all real numbers, as follows. g(x)= 1 3 x^ 2 -4&ifx ne2\\ -4&ifx=2 Find g(- 3), g(2) and g(4) .

Answer 1

To evaluate a piecewise function we need to correctly choose the correct expression for a given value of x.

In this case for any value of x different from 2 we need to use the expression:

`(1)/(3)x^2-4`

And if x=2 the value of the function is -4. With this in mind we have:

`\begin{gathered} g(-3)=(1)/(3)(-3)^2-4=(9)/(3)-4=3-4=-1 \\ g(2)=-4 \\ g(4)=(1)/(3)(4)^2-4=(16)/(3)-4=(16-12)/(3)=(4)/(3) \end{gathered}`

Therefore:

`\begin{gathered} g(-3)=-1 \\ g(2)=-4 \\ g(4)=(4)/(3) \end{gathered}`