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Find [tex]\( f(-3) \)[/tex] in this piecewise function:

[tex]\[
f(x) =
\begin{cases}
-2x + 5 & \text{if } x \ \textless \ 4 \\
\frac{x}{4} - 4 & \text{if } x \geq 4
\end{cases}
\][/tex]

[tex]\( f(-3) = \)[/tex] ?

Sagot :

GinnyAnswer
To solve for [tex]\( f(-3) \)[/tex] in the given piecewise function, let's follow these steps:

We are given the piecewise function:
[tex]\[ \begin{cases} y = -2x + 5 & \text{if } x < 4 \\ y = \frac{x}{4} - 4 & \text{if } x \geq 4 \end{cases} \][/tex]

Step 1: Determine which part of the piecewise function to use.
Since we need to find [tex]\( f(-3) \)[/tex], we substitute [tex]\( x = -3 \)[/tex].

Step 2: Identify the relevant piece of the function.
We check the condition [tex]\( x < 4 \)[/tex]. Since [tex]\( -3 < 4 \)[/tex] is true, we use the equation [tex]\( y = -2x + 5 \)[/tex].

Step 3: Substitute [tex]\( x = -3 \)[/tex] into the appropriate piece of the function.
[tex]\[ y = -2(-3) + 5 \][/tex]

Step 4: Calculate the result step-by-step.
[tex]\[ -2(-3) + 5 = 6 + 5 = 11 \][/tex]

Thus, the value of [tex]\( f(-3) \)[/tex] is:
[tex]\[ f(-3) = 11 \][/tex]

Therefore, [tex]\( f(-3) = 11 \)[/tex].
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