Answered

The function [tex]\( g(x) \)[/tex] is defined as shown.

[tex]\[
g(x) = \left\{
\begin{array}{ll}
x - 1, & \text{if } -2 \leq x \ \textless \ -1 \\
2x + 3, & \text{if } -1 \leq x \ \textless \ 3 \\
6 - x, & \text{if } x \geq 3
\end{array}
\right.
\][/tex]

What is the value of [tex]\( g(3) \)[/tex]?

A. 2
B. 3
C. 9
D. 14



Answer :

GinnyAnswer
To determine the value of [tex]\( g(3) \)[/tex] for the given piecewise function

[tex]\[ g(x) = \begin{cases} x - 1 & \text{if } -2 \leq x < -1 \\ 2x + 3 & \text{if } -1 \leq x < 3 \\ 6 - x & \text{if } x \geq 3 \end{cases} \][/tex]

we need to identify which part of the piecewise function applies when [tex]\( x = 3 \)[/tex].

Let's examine the conditions:

1. [tex]\( -2 \leq x < -1 \)[/tex]: This applies when [tex]\( x \)[/tex] is between -2 (inclusive) and -1 (exclusive). It does not apply to [tex]\( x = 3 \)[/tex].
2. [tex]\( -1 \leq x < 3 \)[/tex]: This applies when [tex]\( x \)[/tex] is between -1 (inclusive) and 3 (exclusive). It does not apply to [tex]\( x = 3 \)[/tex].
3. [tex]\( x \geq 3 \)[/tex]: This applies when [tex]\( x \)[/tex] is greater than or equal to 3. Since [tex]\( x = 3 \)[/tex], this condition is met.

The relevant part of the piecewise function for [tex]\( x = 3 \)[/tex] is:
[tex]\[ g(x) = 6 - x \][/tex]

Substituting [tex]\( x = 3 \)[/tex] into this equation, we get:
[tex]\[ g(3) = 6 - 3 = 3 \][/tex]

Therefore, the value of [tex]\( g(3) \)[/tex] is [tex]\( \boxed{3} \)[/tex].

Other Questions