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Relations and Functions — MATHS STD 11 Science — Question

Rajasthan BoardEnglish MediumSTD 11 ScienceMATHSRelations and Functions2 Marks
Question
If $\text{f(x)}=\frac{\text{x}-1}{\text{x}+1},$ then show that.
$\text{f}\Big(\frac{-1}{\text{x}}\Big)=\frac{-1}{\text{f(x)}}$
✓

Answer

Given that: $\text{f(x)}=\frac{\text{x}-1}{\text{x}+1}$
$\text{f}\Big(\frac{-1}{\text{x}}\Big)=\frac{-\frac{1}{\text{x}}-1}{-\frac{1}{\text{x}}+1}=\frac{-\big(\frac{1}{\text{x}}+1\big)}{-\big(\frac{1}{\text{x}}-1\big)}=\frac{1+\text{x}}{1-\text{x}}=\frac{1}{\frac{1-\text{x}}{1+\text{x}}}$
$=\frac{1}{-\big(\frac{\text{x}-1}{\text{x}+1}\big)}=\frac{-1}{\text{f(x)}}$
Hence, $\text{f}\Big(-\frac{1}{\text{x}}\Big)=\frac{-1}{\text{f(x)}}.$

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