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If f(x)=2x3−2, f(x)=2x^3-2, what is the value of f(−3)? f(-3)?

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Full solution

Q. If f(x)=2x3−2, f(x)=2x^3-2, what is the value of f(−3)? f(-3)?
  1. Identify Function and Input: Identify the function and the input value.\newlineWe are given the function f(x)=2x3−2f(x) = 2x^3 - 2 and we need to find the value of this function when x=−3x = -3.
  2. Substitute Input into Function: Substitute the input value into the function. f(−3)=2(−3)3−2f(-3) = 2(-3)^3 - 2
  3. Calculate Value of (−3)3(-3)^3: Calculate the value of (−3)3(-3)^3.(−3)3=−3×−3×−3=−27(-3)^3 = -3 \times -3 \times -3 = -27
  4. Multiply Result by 22: Multiply the result by 22, as per the function definition.\newline2×(−27)=−542 \times (-27) = -54
  5. Subtract 22 from Result: Subtract 22 from the result obtained in Step 44.\newlinef(−3)=−54−2=−56f(-3) = -54 - 2 = -56

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