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If f(x) = { x^2, x < 0; 2x + 3, x >= 0 }, find f(0).

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Question: If f(x) = { x^2, x < 0; 2x + 3, x >= 0 }, find f(0).

Options:

  1. 0
  2. 3
  3. 1
  4. undefined

Correct Answer: 3

Solution: 

At x = 0, we use the second piece: f(0) = 2(0) + 3 = 3.

If f(x) = { x^2, x < 0; 2x + 3, x >= 0 }, find f(0).

Practice Questions

Q1
If f(x) = { x^2, x < 0; 2x + 3, x >= 0 }, find f(0).
  1. 0
  2. 3
  3. 1
  4. undefined

Questions & Step-by-Step Solutions

If f(x) = { x^2, x < 0; 2x + 3, x >= 0 }, find f(0).
  • Step 1: Identify the function f(x) which has two parts: one for x < 0 and another for x >= 0.
  • Step 2: Since we need to find f(0), we look at the condition for x >= 0.
  • Step 3: Use the second part of the function, which is 2x + 3, because 0 is greater than or equal to 0.
  • Step 4: Substitute 0 into the equation: f(0) = 2(0) + 3.
  • Step 5: Calculate the result: 2(0) = 0, so f(0) = 0 + 3 = 3.
  • Piecewise Functions – Understanding how to evaluate functions defined by different expressions based on the input value.
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