Question

Suppose that the function g is defined for all real numbers

Answer 1

Given:

`g(x)=\begin{cases}(1)/(2)x^2-5,x\\e2 \\ 4,x=2\end{cases}`

To find g(-4), we will take the function when x is not equal to 2, therefore,

`\begin{gathered} g(-4)=(1)/(2)(-4)^2-5 \\ =(1)/(2)\lbrack16\rbrack-5 \\ =8-5 \\ =3 \end{gathered}`

Therefore, g( - 4) = 3

To find g(2),

The value of function at x = 2 is 4 so g(2)=4

To find g( 5):

`\begin{gathered} g(5)=(1)/(2)\lbrack5^2\rbrack-5 \\ =(25)/(2)-5 \\ =(25-10)/(2) \\ =(15)/(2) \\ =7.5 \end{gathered}`

Therefore, g(5) = 7.5