Sure, I will guide you through the solution step by step.
The function given is:
[tex]\[
y = \begin{cases}
7 & \text{if } x \leq 1 \\
10 & \text{if } x > 1
\end{cases}
\][/tex]
### Part (a): Find [tex]\( f(-1) \)[/tex]
To find [tex]\( f(-1) \)[/tex], we need to determine which condition of the piecewise function applies when [tex]\( x = -1 \)[/tex].
1. Check the first condition: [tex]\( x \leq 1 \)[/tex]
2. Since [tex]\(-1 \leq 1\)[/tex] is true, we use the first part of the piecewise function.
According to the first condition, when [tex]\( x \leq 1 \)[/tex]:
[tex]\[
f(x) = 7
\][/tex]
Thus:
[tex]\[
f(-1) = 7
\][/tex]
Therefore, the correct choice for part (a) is:
A. [tex]\( f(-1) = 7 \)[/tex]
### Part (b): Find [tex]\( f(2) \)[/tex]
To find [tex]\( f(2) \)[/tex], we need to determine which condition of the piecewise function applies when [tex]\( x = 2 \)[/tex].
1. Check the second condition: [tex]\( x > 1 \)[/tex]
2. Since [tex]\( 2 > 1 \)[/tex] is true, we use the second part of the piecewise function.
According to the second condition, when [tex]\( x > 1 \)[/tex]:
[tex]\[
f(x) = 10
\][/tex]
Thus:
[tex]\[
f(2) = 10
\][/tex]
Therefore, the correct choice for part (b) is:
A. [tex]\( f(2) = 10 \)[/tex]
So in summary:
a. [tex]\( f(-1) = 7 \)[/tex]
b. [tex]\( f(2) = 10 \)[/tex]
