Question

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

Answer 1

Option B:

f(3) = 5

Solution:

Given function:

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

• If x value is less than –2, that is –3, –4, –5, –6, ... then f(x) = –x².
• If x value is greater than or equal to –2 and less than 0, that is –2 and –1 then f(x) = 3.
• If x value is greater than or equal to 0, that is 0, 1, 2, 3,... then f(x) = x +2.

To find the value of f(3):

Here x value is 3 which is greater than 0 (3 > 0).

Therefore, f(x) = x + 2.

Substitute x = 3 in the above function.

f(3) = 3 + 2

f(3) = 5

Hence option B is the correct answer.