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Evaluate the piecewise function at the given value of the independent variable:

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

Find [tex]\( f(8) \)[/tex].

A. 42 and 28
B. 28
C. 42
D. 70

Answer :

To evaluate the piecewise function [tex]\( f(x) \)[/tex] at [tex]\( x = 8 \)[/tex], follow these steps:

1. Identify the correct piece of the function:
- The function is defined as:
[tex]\[
f(x) = \begin{cases}
4x - 4 & \text{if } x < 5 \\
5x + 2 & \text{if } x \geq 5
\end{cases}
\][/tex]
- Since [tex]\( x = 8 \)[/tex], which is greater than or equal to 5, we use the second piece of the function: [tex]\( f(x) = 5x + 2 \)[/tex].

2. Substitute the value [tex]\( x = 8 \)[/tex] into the correct piece of the function:
[tex]\[
f(8) = 5(8) + 2
\][/tex]

3. Perform the calculations:
[tex]\[
f(8) = 40 + 2
\][/tex]
[tex]\[
f(8) = 42
\][/tex]

Thus, the value of the function at [tex]\( x = 8 \)[/tex] is 42.

The correct answer is C. 42.

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