For the following function, find the value of (a) [tex]$f(-1)$[/tex] and (b) [tex]$f(2)$[/tex], if possible.

[tex]\[ y=\left\{
\begin{aligned}
7 & \text{ if } x \leq 1 \\
10 & \text{ if } x \ \textgreater \ 1
\end{aligned}\right.
\][/tex]

a. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. [tex]$f(-1) = \square$[/tex] (Simplify your answer.)
B. There is no solution.

b. Select the correct choice below and, if necessary, fill in the answer box within your choice.

A. [tex]$f(2) = \square$[/tex] (Simplify your answer.)
B. There is no solution.



Answer :

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]