Set, Relations and FunctionsPYQ June 19Question 1960 of 217
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If f(x)=x2\displaystyle f(x) = x^2 and g(x)=x\displaystyle g(x) = \sqrt{x}, then

Options

Agof(3)=3\displaystyle gof(3) = 3
Bgof(9)=3\displaystyle gof(9) = 3
Cgof(9)=9\displaystyle gof(9) = 9
Dgof(3)=9\displaystyle gof(3) = 9
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Correct Answer

✅ Option a — gof(3)=3\displaystyle gof(3) = 3

All Options:

  • Agof(3)=3\displaystyle gof(3) = 3
  • Bgof(9)=3\displaystyle gof(9) = 3
  • Cgof(9)=9\displaystyle gof(9) = 9
  • Dgof(3)=9\displaystyle gof(3) = 9

Detailed Solution & Explanation

We are given functions f(x)=x2\displaystyle f(x) = x^2 and g(x)=x\displaystyle g(x) = \sqrt{x}.
Let's find the composite function gof(x)\displaystyle gof(x):
gof(x)=g(f(x))=g(x2)=x2=x(for x≥0)gof(x) = g(f(x)) = g(x^2) = \sqrt{x^2} = x \quad (\text{for } x \ge 0)
Let's evaluate the options:
- For Option A: gof(3)=3\displaystyle gof(3) = 3. Since 3≥0\displaystyle 3 \ge 0, 32=3\displaystyle \sqrt{3^2} = 3. This statement is **TRUE**.
- For Option B: gof(9)=3\displaystyle gof(9) = 3. But gof(9)=92=9≠3\displaystyle gof(9) = \sqrt{9^2} = 9 \neq 3. (False)
- For Option C: gof(9)=9\displaystyle gof(9) = 9. Since 9≥0\displaystyle 9 \ge 0, 92=9\displaystyle \sqrt{9^2} = 9. This statement is also **TRUE**.
- For Option D: gof(3)=9\displaystyle gof(3) = 9. But gof(3)=3≠9\displaystyle gof(3) = 3 \neq 9. (False)
Since Option A and Option C are both mathematically correct, we follow the textbook's key which lists Option A.
Hence, **Option A** is the correct answer.

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