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Functions — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHSFunctions1 Mark
MCQ
If $\text{x}\neq1$ and $\text{f(x)}=\frac{\text{x}+1}{\text{x}-1}$ is a real function, then $\text{f}(\text{f}(\text{f(2)}))$ is:
  • A
    1
  • B
    2
  • ✓
    3
  • D
    4
✓

Answer

Correct option: C.
3
$\text{f(x)}=\frac{\text{x}+1}{\text{x}-1}$
$\text{f}(\text{f}(\text{f(2)}))$
$=\text{f}\Big(\text{f}\Big(\frac{2+1}{2-1}\Big)\Big)$
$=\text{f}(\text{f}(3))$
$=\text{f}\Big(\frac{3+1}{3-1}\Big)$
$=\text{f}(2)=3$

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