Download App

Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsFunctions5 Marks
Question
If $\text{f(x)}=\frac{1}{1-\text{x}},$ show that $\text{f}\big[\text{f}\{\text{f(x)}\}\big]=\text{x}$
✓

Answer

We have,
$\text{f(x)}=\frac{1}{1-\text{x}}$
Now, $\text{f}\{\text{f}(\text{x})\}=\text{f}\Big\{\frac{1}{1-\text{x}}\Big\}$
$=\frac{1}{1-\frac{1}{1-\text{x}}}$
$=\frac{1}{\frac{1-\text{x}-1}{1-\text{x}}}$
$=\frac{1-\text{x}}{-\text{x}}$
$=\frac{\text{x}-1}{\text{x}}$
$\therefore\ \text{f}\big[\text{f}\{\text{f(x)}\}\big]=\text{f}\Big\{\frac{1}{1-\text{x}}\Big\}$
$=\frac{1}{1-\big(\frac{\text{x}-1}{\text{x}}\big)}$
$=\frac{1}{\frac{\text{x}-\text{x}+1}{\text{x}}}$
$=\frac{\text{x}}{1}$
$=\text{x}$
$\therefore\ \text{f}\big[\text{f}\{\text{f(x)}\}\big]=\text{x}$ Hence, proved.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Functions→Functions — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

Solve the following equations:
$2\sin^{2}\text{x}=3\cos\text{x},0\leq\text{x}\leq2\pi$
→
Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow0}\frac{\text{x}\tan\text{x}}{1-\cos2\text{x}}$
→
If $\tan\text{x}=\frac{\text{b}}{\text{a}},$ then find the value of $\sqrt{\frac{\text{a}+\text{b}}{\text{a}-\text{b}}}+\sqrt{\frac{\text{a}-\text{b}}{\text{a}+\text{b}}}$
→
A student obtained the mean and standard deviation of $100$ observations as $40$ and $5.1$ respectively. It was later found that one observation was wrongly copied as $50$, the correct figure being $40.$ Find the correct mean and $S.D.$
→
Let $a_n $ be the nth term of the G.P. of positive numbers. Let $\sum\limits_{\text{n}=1}^{100}\text{a}_{2\text{n}}=\alpha\text{ and}\sum\limits_{\text{n}=1}^{10}\text{a}_{2\text{n}-1}=\beta,$ such that $\alpha\neq\beta.$ Prove that the common ratio of the G.P. is $\frac{\alpha}{\beta}$
→
Show that $\text{x}^2+\text{xy}+\text{y}^2,\ \text{z}^2+\text{zx}+\text{x}^2$ and $\text{y}^2+\text{yz}+\text{z}^2$ are consecutive terms of an A.P., if x, y and z are in A.P.
→
While calculating the mean and variance of 10 readings, a student wrongly used the reading of 52 for the correct reading 25. He obtained the mean and variance as 45 and 16 respectively. Find the correct mean and the variance.
→
Determine the domain and range of the relation R defined by:
$\text{R}=\{(\text{x, x,}+5):\text{x}\in\{0,1,2,3,4,5\}\}$
→
Match the statements of Column $A$ and Column $B.$
  Column $A$   Column $B$
$a.$ The polar form of $\text{i}+\sqrt{3}$ is $i.$ Perpendicular bisector of segment joining $(– 2, 0)$ and $(2, 0).$
$b.$ The amplitude of $-1+\sqrt{-3}$ is $ii.$ On or outside the circle having centre at $(0, – 4)$ and radius $3.$
$c.$ If $|z + 2| = |z - 2|,$ then locus of $z$ is $iii.$ $\frac{2\pi}{3}$
$d.$ If $|z + 2i| = |z - 2i|,$ then locus of $z$ is $iv.$ Perpendicular bisector of segment joining $(0, – 2)$ and $(0, 2).$
$e.$ Region represented by $|\text{z}+4\text{i}|\geq3$ is $v.$ $2\Big(\cos\frac{\pi}{6}+\text{i}\sin\frac{\pi}{6}\Big)$
$f.$ Region represented by $|\text{z}+4|\leq3$ is $vi.$ On or inside the circle having centre $(– 4, 0)$ and radius $3$ units.
$g.$ Conjugate of $\frac{1+2\text{i}}{1-\text{i}}$ lies in $vii.$ First quadrant.
$h.$ Reciprocal of $1 - i$ lies in $viii.$ Third quadrant.
→
calculate the mean deviation from the median of the following frequency distribution:
Hights in inches
58
59
60
61
62
63
64
65
66
No. of students
15
20
32
35
35
22
20
10
8
→