Domain, Co-domain and Range of Function
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Sets, Relation and Function

117325 Considering only the principal values of the trigonometric functions, the domain of the function \(f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)\) is :

1 \(\left(-\infty, \frac{1}{4}\right]\)
2 \(\left[-\frac{1}{4}, \infty\right)\)
3 \(\left(\frac{-1}{3}, \infty\right)\)
4 \(\left(-\infty, \frac{1}{3}\right]\)
Shift-I
Sets, Relation and Function

117326 If the domain of the function \(f(x)=\frac{[x]}{1+x^2}\), where \([x]\) is greatest integer \(\leq x\), is \([2,6)\), then its range is

1 \(\left(\frac{5}{37}, \frac{2}{5}\right]\)
2 \(\left(\frac{5}{26}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
3 \(\left(\frac{5}{26}, \frac{2}{5}\right]\)
4 \(\left(\frac{5}{37}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
Shift-I
Sets, Relation and Function

117335 The range of the function \(f(x)\) \(=-\sqrt{-5-6 x-x^2}\) is

1 \([-2,2]\)
2 \([-\infty,-2]\)
3 \([2, \infty]\)
4 \([-2,0]\)
Shift-2
Sets, Relation and Function

117327 Let \(f: R-\{2,6\} \rightarrow R\) be real valued function defined as \(f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}\). Then range of \(f\) is

1 \(\left(-\infty,-\frac{21}{4}\right] \cup\left[\frac{21}{4}, \infty\right)\)
2 \(\left(-\infty,-\frac{21}{4}\right] \cup[0, \infty]\)
3 \(\left(-\infty,-\frac{21}{4}\right) \cup(0, \infty)\)
4 \(\left(-\infty,-\frac{21}{4}\right] \cup(1, \infty)\)
Shift-II
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Sets, Relation and Function

117325 Considering only the principal values of the trigonometric functions, the domain of the function \(f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)\) is :

1 \(\left(-\infty, \frac{1}{4}\right]\)
2 \(\left[-\frac{1}{4}, \infty\right)\)
3 \(\left(\frac{-1}{3}, \infty\right)\)
4 \(\left(-\infty, \frac{1}{3}\right]\)
Shift-I
Sets, Relation and Function

117326 If the domain of the function \(f(x)=\frac{[x]}{1+x^2}\), where \([x]\) is greatest integer \(\leq x\), is \([2,6)\), then its range is

1 \(\left(\frac{5}{37}, \frac{2}{5}\right]\)
2 \(\left(\frac{5}{26}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
3 \(\left(\frac{5}{26}, \frac{2}{5}\right]\)
4 \(\left(\frac{5}{37}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
Shift-I
Sets, Relation and Function

117335 The range of the function \(f(x)\) \(=-\sqrt{-5-6 x-x^2}\) is

1 \([-2,2]\)
2 \([-\infty,-2]\)
3 \([2, \infty]\)
4 \([-2,0]\)
Shift-2
Sets, Relation and Function

117327 Let \(f: R-\{2,6\} \rightarrow R\) be real valued function defined as \(f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}\). Then range of \(f\) is

1 \(\left(-\infty,-\frac{21}{4}\right] \cup\left[\frac{21}{4}, \infty\right)\)
2 \(\left(-\infty,-\frac{21}{4}\right] \cup[0, \infty]\)
3 \(\left(-\infty,-\frac{21}{4}\right) \cup(0, \infty)\)
4 \(\left(-\infty,-\frac{21}{4}\right] \cup(1, \infty)\)
Shift-II
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Sets, Relation and Function

117325 Considering only the principal values of the trigonometric functions, the domain of the function \(f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)\) is :

1 \(\left(-\infty, \frac{1}{4}\right]\)
2 \(\left[-\frac{1}{4}, \infty\right)\)
3 \(\left(\frac{-1}{3}, \infty\right)\)
4 \(\left(-\infty, \frac{1}{3}\right]\)
Shift-I
Sets, Relation and Function

117326 If the domain of the function \(f(x)=\frac{[x]}{1+x^2}\), where \([x]\) is greatest integer \(\leq x\), is \([2,6)\), then its range is

1 \(\left(\frac{5}{37}, \frac{2}{5}\right]\)
2 \(\left(\frac{5}{26}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
3 \(\left(\frac{5}{26}, \frac{2}{5}\right]\)
4 \(\left(\frac{5}{37}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
Shift-I
Sets, Relation and Function

117335 The range of the function \(f(x)\) \(=-\sqrt{-5-6 x-x^2}\) is

1 \([-2,2]\)
2 \([-\infty,-2]\)
3 \([2, \infty]\)
4 \([-2,0]\)
Shift-2
Sets, Relation and Function

117327 Let \(f: R-\{2,6\} \rightarrow R\) be real valued function defined as \(f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}\). Then range of \(f\) is

1 \(\left(-\infty,-\frac{21}{4}\right] \cup\left[\frac{21}{4}, \infty\right)\)
2 \(\left(-\infty,-\frac{21}{4}\right] \cup[0, \infty]\)
3 \(\left(-\infty,-\frac{21}{4}\right) \cup(0, \infty)\)
4 \(\left(-\infty,-\frac{21}{4}\right] \cup(1, \infty)\)
Shift-II
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Sets, Relation and Function

117325 Considering only the principal values of the trigonometric functions, the domain of the function \(f(x)=\cos ^{-1}\left(\frac{x^2-4 x+2}{x^2+3}\right)\) is :

1 \(\left(-\infty, \frac{1}{4}\right]\)
2 \(\left[-\frac{1}{4}, \infty\right)\)
3 \(\left(\frac{-1}{3}, \infty\right)\)
4 \(\left(-\infty, \frac{1}{3}\right]\)
Shift-I
Sets, Relation and Function

117326 If the domain of the function \(f(x)=\frac{[x]}{1+x^2}\), where \([x]\) is greatest integer \(\leq x\), is \([2,6)\), then its range is

1 \(\left(\frac{5}{37}, \frac{2}{5}\right]\)
2 \(\left(\frac{5}{26}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
3 \(\left(\frac{5}{26}, \frac{2}{5}\right]\)
4 \(\left(\frac{5}{37}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
Shift-I
Sets, Relation and Function

117335 The range of the function \(f(x)\) \(=-\sqrt{-5-6 x-x^2}\) is

1 \([-2,2]\)
2 \([-\infty,-2]\)
3 \([2, \infty]\)
4 \([-2,0]\)
Shift-2
Sets, Relation and Function

117327 Let \(f: R-\{2,6\} \rightarrow R\) be real valued function defined as \(f(x)=\frac{x^2+2 x+1}{x^2-8 x+12}\). Then range of \(f\) is

1 \(\left(-\infty,-\frac{21}{4}\right] \cup\left[\frac{21}{4}, \infty\right)\)
2 \(\left(-\infty,-\frac{21}{4}\right] \cup[0, \infty]\)
3 \(\left(-\infty,-\frac{21}{4}\right) \cup(0, \infty)\)
4 \(\left(-\infty,-\frac{21}{4}\right] \cup(1, \infty)\)
Shift-II
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