Question

Evaluate when f(-3) and f(7)

Answer 1

Answers:

• f(-3) = -6
• f(7) = 20

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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 $x \le 4$, then f(x) = 2x

The input x = -3 satisfies the inequality $x \le 4$, 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 $x \le 4$, then f(x) = h(x)". Though this might be a more wordy definition.