Question

The equation of the piecewise function f(x) is below. What is the value of f(3)?

Answer 1

Option B: 5 is the value of f(3)

Step-by-step explanation:

The equation of the piecewise function is given by

`f(x)=\left\{\begin{aligned}-x^(2), & x<-2 \\3, &-2 \leq x<0 \\x+2, & x \geq 0\end{aligned}\right.`

We need to find the value of
`f(3)`

The value of the function f can be determined when
`x=3` by identifying in which interval does the value of
`x=3` lie in the piecewise function.

Thus,
`x=3` lies in the interval
`x\geq 0` , the function f is given by

`f(x)=x+2`

Substituting
`x=3` in the function
`f(x)=x+2`, we get,

`f(3)=3+2`

`f(3)=5`

Thus, the value of
`f(3)` is 5.

Therefore, Option B is the correct answer.