Question

Two piecewise functions are shown below. What is the value of 6f * (- 2) + 3g * (1) ?

Answer 1

First part

To find the value of f(-2), we replace x = -2 into the second piece of the function. Then, we operate.

`\begin{gathered} f(-2)=(1)/(3)(-2)^3 \\ f(-2)=(1)/(3)(-8) \\ f(-2)=-(8)/(3) \end{gathered}`

Second part

To find the value of g(1), we replace x = 1 into the first piece of the function. Then, we operate.

`\begin{gathered} g(1)=2|1-1|+3 \\ g(1)=2|0|+3 \\ g(1)=2\cdot0+3 \\ g(1)=0+3 \\ g(1)=3 \end{gathered}`

Finally, we find the value of the given expression:

`\begin{gathered} 6f(-2)+3g(1)=6\cdot-(8)/(3)+3\cdot3 \\ 6f(-2)+3g(1)=-(6\cdot8)/(3)+9 \\ 6f(-2)+3g(1)=-(48)/(3)+9 \\ 6f(-2)+3g(1)=-16+9 \\ 6f(-2)+3g(1)=-7 \end{gathered}`