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# Piecewise function

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Let

f(x) = -x-3 if x <= -7

f(x) = 2x + 1 if x > -7

Find the sum of all values of $x$ such that f(x) = 0.

May 12, 2022

#1
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Suppose x <= -7. When f(x) = 0, -x - 3 = 0. This means x = -3, which is not <= -7. This root is rejected.

Suppose x > -7. When f(x) = 0, 2x + 1 = 0. This means $$x = -\dfrac{\boxed{\phantom{\text{aaaaa}}}}{\boxed{\phantom{\text{aaaaa}}}}$$.

Therefore, the sum of all values of x such that f(x) = 0 is $$-\dfrac{\boxed{\phantom{\text{aaaaa}}}}{\boxed{\phantom{\text{aaaaa}}}}$$, as it is the only solution to f(x) = 0.