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If [tex]f(x) = 5[/tex] when [tex]x \leq 2[/tex] and [tex]f(x) = 2x - 3[/tex] when [tex]x \ \textgreater \ 2[/tex], please evaluate [tex]f(-3)[/tex].

A. 7
B. None of these
C. 5
D. 9
E. -5
F. -9

Sagot :

GinnyAnswer
To evaluate [tex]\( f(-3) \)[/tex], we need to determine which definition of the piecewise function to use based on the value of [tex]\( x \)[/tex].

The function [tex]\( f(x) \)[/tex] is defined as:
[tex]\[ f(x) = 5 \text{ when } x \leq 2 \][/tex]
[tex]\[ f(x) = 2x - 3 \text{ when } x > 2 \][/tex]

Given [tex]\( x = -3 \)[/tex]:
1. First, we check the condition [tex]\( x \leq 2 \)[/tex].
2. Since [tex]\(-3 \leq 2\)[/tex] is true, we use the first part of the piecewise function [tex]\( f(x) = 5 \)[/tex].

Therefore, [tex]\( f(-3) \)[/tex] is evaluated as 5.

The correct answer is:
(C) 5
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