We have to calculate the value of:
[tex]4\cdot f(\frac{1}{2})+2\cdot f(3)[/tex]
We have to look for the value of f(1/2) and f(3) in the definition of f(x).
For f(1/2), x is 1/2 and is between 0 and 3, so f(x) is:
[tex]\begin{gathered} f(x)=x^2-2 \\ f(\frac{1}{2})=(\frac{1}{2})^2-2 \\ f(\frac{1}{2})=\frac{1}{4}-2 \\ f(\frac{1}{2})=\frac{1}{4}-\frac{8}{4} \\ f(\frac{1}{2})=-\frac{7}{4} \end{gathered}[/tex]
For f(3), it falls in the interval for x ≥ 3, so f(3) can be calculated as:
[tex]\begin{gathered} f(x)=3x-4 \\ f(3)=3(3)-4 \\ f(3)=9-4 \\ f(3)=5 \end{gathered}[/tex]
Then, we can now calculate the value of the expression as:
[tex]\begin{gathered} 4f(\frac{1}{2})+2f(3) \\ 4\cdot(-\frac{7}{4})+2\cdot5 \\ -7+10 \\ 3 \end{gathered}[/tex]
Answer: the expression is equal to 3.
