Explore a diverse range of topics and get answers from knowledgeable individuals on IDNLearn.com. Ask your questions and receive detailed and reliable answers from our experienced and knowledgeable community members.

Given the piecewise function:

[tex]\[
f(x)=\left\{
\begin{array}{cc}
x^2 & \text{if } x \leq 3 \\
2x - 4 & \text{if } x \ \textgreater \ 3
\end{array}
\right\}
\][/tex]

If [tex]\( x = -4 \)[/tex], then [tex]\( f(x) = \square \)[/tex]

Answer: [tex]\( \square \)[/tex]


Sagot :

To find the value of [tex]\( f(x) \)[/tex] when [tex]\( x = -4 \)[/tex], we need to determine which piece of the piecewise function to use based on the given value of [tex]\( x \)[/tex].

The piecewise function is defined as:
[tex]\[ f(x) = \begin{cases} x^2 & \text{if } x \leq 3 \\ 2x - 4 & \text{if } x > 3 \end{cases} \][/tex]

Given [tex]\( x = -4 \)[/tex]:

1. We observe that [tex]\(-4 \leq 3\)[/tex].
2. Since [tex]\(-4\)[/tex] is less than or equal to [tex]\(3\)[/tex], we use the first part of the piecewise function, which is [tex]\( f(x) = x^2 \)[/tex].

Now, we substitute [tex]\( x = -4 \)[/tex] into this part of the function:

[tex]\[ f(-4) = (-4)^2 \][/tex]

Calculating the square of [tex]\(-4\)[/tex]:

[tex]\[ (-4)^2 = 16 \][/tex]

Thus:

[tex]\[ f(-4) = 16 \][/tex]

Therefore, the value of [tex]\( f(x) \)[/tex] when [tex]\( x = -4 \)[/tex] is [tex]\( \boxed{16} \)[/tex].