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Functions MATHS - Functions

Rajasthan Board (RBSE) - STD 11 Science - MATHS (Rajasthan - English Medium). 143 questions in this chapter.

Question types

Functions question types

143 questions across 5 question groups — pick any mix to generate a MATHS paper with step-by-step answer keys.

143
Questions
5
Question groups
5
Question types
Sample Questions

Functions questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
The domain of definition of the function $\text{f(x)}=\sqrt{\text{x}-1}+\sqrt{3-\text{x}}$ is:
  1. $[1,\infty)$
  2. $\big(-\infty,3\big)$
  3. $(1,3)$
  4. $\big[1,3\big]$
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Q 2M.C.Q (1 Marks)1 Mark
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:
  1. 1
  2. 2
  3. 3
  4. 4
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Q 3M.C.Q (1 Marks)1 Mark
The domain of definition of $\text{f(x)}=\sqrt{\frac{\text{x}+3}{(2-\text{x})(\text{x}-5)}}$ is:
  1. $(-\infty,-3]\cup(2,5)$
  2. $(-\infty,-3]\cup(2,5)$
  3. $(-\infty,-3]\cup[2,5]$
  4. None of these.
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Q 4M.C.Q (1 Marks)1 Mark
The range of the function $\text{f(x)}=\frac{\text{x}^2-\text{x}}{\text{x}^2+2\text{x}}$ is:
  1. $\text{R}$
  2. $\text{R}-\{1\}$
  3. $\text{R}-\Big\{\frac{1}{2},1\Big\}$
  4. None of these.
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Q 5M.C.Q (1 Marks)1 Mark
If $\text{e}^{\text{f(x)}}=\frac{10+\text{x}}{10-\text{x}},\text{ x}\in(-10,10)$ and $\text{f(x)}=\text{kf}\Big(\frac{200\text{x}}{100+\text{x}^2}\Big),$ then k =
  1. 0.5
  2. 0.6
  3. 0.7
  4. 0.8
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Q 61 Marks Question1 Mark
Let $\text{f(x)}=\frac{\alpha\text{x}}{\text{x}+1},\text{x}\neq-1.$ Then write the value of $\alpha$ satisfying $\text{f}(\text{f(x)})=\text{x}$ for all $\text{x}\neq-1$
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Q 71 Marks Question1 Mark
If f is a real function satisfying $\text{f}\Big(\text{x}+\frac{1}{\text{x}}\Big)=\text{x}^2+\frac{1}{\text{x}^2}$ for all $\text{x}\in\text{R}-\{0\},$ then write the expression for f(x).
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Q 163 Marks Question3 Marks
If $\text{f(x)}=\frac{\text{x}-1}{\text{x}+1},$ then show that:
  1. $\text{f}\Big(\frac{1}{\text{x}}\Big)=-\text{f(x)}$
  2. $\text{f}\Big(-\frac{1}{\text{x}}\Big)=-\frac{1}{\text{f(x)}}$
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Q 225 Marks Questions5 Marks
Let $\text{f}:[0,\infty)\rightarrow\text{R}$ and $\text{g}:\text{R}\rightarrow\text{R}$ be defined by $\text{f(x)}=\sqrt{\text{x}}$ and g(x) = x. Find f + g, g - g, fg and $\frac{\text{f}}{\text{g}}$
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Q 235 Marks Questions5 Marks
Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
g - f
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Q 245 Marks Questions5 Marks
Let f and g be two real functions defined by $\text{f(x)}=\sqrt{\text{x}+1}$ and $\text{g(x)}=\sqrt{9-\text{x}^2}$ Then describe the following functions:
$\text{f}^2+7\text{f}$
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