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QuestionFind xx such that f(x)=−3f(x) = -3 for the function f(x)=∣x∣f(x) = |x|.

Studdy Solution

STEP 1

Assumptions1. The function is defined as f(x)=∣x∣f(x)=|x| . We are given that f(x)=−3f(x)=-3

STEP 2

The absolute value function f(x)=∣x∣f(x)=|x| is defined as followsf(x)={xif x≥0−xif x<0f(x) =\begin{cases}x & \text{if } x \geq0 \\ -x & \text{if } x <0\end{cases}

STEP 3

We are given that f(x)=−3f(x)=-3. However, the absolute value of any real number is always non-negative. This means that f(x)f(x) can never be negative.

STEP 4

Therefore, there is no real number xx for which f(x)=−3f(x)=-3 when f(x)=∣x∣f(x)=|x|.

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