Answers:
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Explanation:
The piecewise function f(x) changes based on what the input is.
We have two cases:
- Case A) if x > 4, then f(x) = 3x-1
- Case B) If [tex]x \le 4[/tex], then f(x) = 2x
The input x = -3 satisfies the inequality [tex]x \le 4[/tex], so we go with case B for this input
f(x) = 2x
f(-3) = 2(-3)
f(-3) = -6
In contrast, the input x = 7 satisfies the inequality x > 4. So we go for case A this time.
f(x) = 3x-1
f(7) = 3(7)-1
f(7) = 21-1
f(7) = 20
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Side note: It might be better to let g(x) = 3x-1 and h(x) = 2x. Then we could further say "If x > 4, then f(x) = g(x) OR if [tex]x \le 4[/tex], then f(x) = h(x)". Though this might be a more wordy definition.
