Set, Relations and FunctionsMTP June 2023 Series IQuestion 1997 of 217
All Questions

If f(x)=x2−5\displaystyle f(x)=x^2-5, evaluate f(3)\displaystyle f(3), f(−4)\displaystyle f(-4), f(5)\displaystyle f(5), and f(1)\displaystyle f(1).

Options

A0,11,20,4\displaystyle 0, 11, 20, 4
B−4,11,−2,4\displaystyle -4, 11, -2, 4
C4,11,20,−4\displaystyle 4, 11, 20, -4
D−2,0,20,5\displaystyle -2, 0, 20, 5
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Correct Answer

✅ Option c — 4,11,20,−4\displaystyle 4, 11, 20, -4

All Options:

  • A0,11,20,4\displaystyle 0, 11, 20, 4
  • B−4,11,−2,4\displaystyle -4, 11, -2, 4
  • C4,11,20,−4\displaystyle 4, 11, 20, -4
  • D−2,0,20,5\displaystyle -2, 0, 20, 5

Detailed Solution & Explanation

Given the function:
f(x)=x2−5f(x) = x^2 - 5
We evaluate the function for each of the given values:

1. **For x=3\displaystyle x = 3**:
f(3)=32−5=9−5=4f(3) = 3^2 - 5 = 9 - 5 = 4
2. **For x=−4\displaystyle x = -4**:
f(−4)=(−4)2−5=16−5=11f(-4) = (-4)^2 - 5 = 16 - 5 = 11
3. **For x=5\displaystyle x = 5**:
f(5)=52−5=25−5=20f(5) = 5^2 - 5 = 25 - 5 = 20
4. **For x=1\displaystyle x = 1**:
f(1)=12−5=1−5=−4f(1) = 1^2 - 5 = 1 - 5 = -4

The evaluated values are 4,11,20,−4\displaystyle 4, 11, 20, -4.

Hence, **Option C** is the correct answer.

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