Question

Given the following piecewise function . f(x)= 3 x &if x<0\\ x^ 2 -2&if 0<= x<3\\ 3x-4&if x>=3 Determine the solution of 4f * (1/2) + 2f * (3)

Answer 1

We have to calculate the value of:

`4\cdot f((1)/(2))+2\cdot f(3)`

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:

`\begin{gathered} f(x)=x^2-2 \\ f((1)/(2))=((1)/(2))^2-2 \\ f((1)/(2))=(1)/(4)-2 \\ f((1)/(2))=(1)/(4)-(8)/(4) \\ f((1)/(2))=-(7)/(4) \end{gathered}`

For f(3), it falls in the interval for x ≥ 3, so f(3) can be calculated as:

`\begin{gathered} f(x)=3x-4 \\ f(3)=3(3)-4 \\ f(3)=9-4 \\ f(3)=5 \end{gathered}`

Then, we can now calculate the value of the expression as:

`\begin{gathered} 4f((1)/(2))+2f(3) \\ 4\cdot(-(7)/(4))+2\cdot5 \\ -7+10 \\ 3 \end{gathered}`

Answer: the expression is equal to 3.