Answered

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Find [tex]\( f(6) \)[/tex] in this piecewise function.

[tex]\[
f(x) =
\begin{cases}
-2x + 8 & \text{if } x \ \textless \ 7 \\
\frac{3}{7}x - 9 & \text{if } x \geq 7
\end{cases}
\][/tex]

[tex]\( f(6) = ? \)[/tex]

Sagot :

GinnyAnswer
To find [tex]\( f(6) \)[/tex] for the given piecewise function, we need to determine which part of the function to use based on the value of [tex]\( x = 6 \)[/tex].

The piecewise function is defined as:

[tex]\[ \begin{cases} y = -2x + 8 & \text{if } x < 7 \\ y = \frac{3}{7}x - 9 & \text{if } x \geq 7 \end{cases} \][/tex]

Since [tex]\( 6 < 7 \)[/tex], we use the first piece of the function, [tex]\( y = -2x + 8 \)[/tex].

Step-by-step, let's calculate [tex]\( f(6) \)[/tex]:

1. Substitute [tex]\( x = 6 \)[/tex] into the equation [tex]\( y = -2x + 8 \)[/tex]:

[tex]\[ y = -2(6) + 8 \][/tex]

2. Perform the multiplication:

[tex]\[ y = -12 + 8 \][/tex]

3. Perform the addition:

[tex]\[ y = -4 \][/tex]

Thus, [tex]\( f(6) = -4 \)[/tex].
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