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Functions — Maths STD 11 Science — Question

Maharashtra BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
Question
If $\text{f(x)}=1-\frac{1}{\text{x}},$ then write the value of $\text{f}\Big(\text{f}\Big(\frac{1}{\text{x}}\Big)\Big)$
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Answer

We have,
$\text{f(x)}=1-\frac{1}{\text{x}}$
Now,
$\text{f}\Big(\text{f}\Big(\frac{1}{\text{x}}\Big)\Big)=\text{f}\bigg[1-\frac{1}{\frac{1}{\text{x}}}\bigg]$
$=\text{f}\big[1-\text{x}\big]$
$=1-\frac{1}{1-\text{x}}$
$=\frac{1-\text{x}-1}{1-\text{x}}$
$=\frac{-\text{x}}{1-\text{x}}$
$\text{f}\Big(\text{f}\Big(\frac{1}{\text{x}}\Big)\Big)=\frac{-\text{x}}{1-\text{x}}$

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