117249
If \(f(x)=8 x^3, g(x)=x^{1 / 3}\), then fog(x) is
1 \(8^3 x\)
2 \(8 x^3\)
3 \(8 \mathrm{x}\)
4 \((8 x)^{1 / 3}\)
Explanation:
C Given \(f(\mathrm{x})=8 \mathrm{x}^3\), \(g(x)=x^{1 / 3}\) The fog \((\mathrm{x})=f(\mathrm{~g}(\mathrm{x}))\) \(=8 \cdot\left[\mathrm{x}^{1 / 3}\right]^3=8 \cdot x\)
Karnataka CET-2017
Sets, Relation and Function
117250
If \(f: R \rightarrow R\) is defined by \(f(x)=\frac{x}{x^2+1}\) find \(\mathbf{f}(\mathbf{f}(2))\).
1 \(\frac{10}{29}\)
2 29
3 \(\frac{1}{29}\)
4 \(\frac{29}{10}\)
Explanation:
A It \(f: R \rightarrow R\) is defined by \(f(\mathrm{x})=\frac{\mathrm{x}}{\mathrm{x}^2+1}\) \(\therefore \quad f(2)=\frac{2}{2^2+1}=\frac{2}{5}\) \(\therefore \quad f(f(2))=f\left(\frac{2}{5}\right)=\frac{2 / 5}{\frac{4}{25}+1}\) \(=\frac{2 / 5}{29 / 25}=\frac{2}{5} \times \frac{25}{29}=\frac{10}{29}\)
117249
If \(f(x)=8 x^3, g(x)=x^{1 / 3}\), then fog(x) is
1 \(8^3 x\)
2 \(8 x^3\)
3 \(8 \mathrm{x}\)
4 \((8 x)^{1 / 3}\)
Explanation:
C Given \(f(\mathrm{x})=8 \mathrm{x}^3\), \(g(x)=x^{1 / 3}\) The fog \((\mathrm{x})=f(\mathrm{~g}(\mathrm{x}))\) \(=8 \cdot\left[\mathrm{x}^{1 / 3}\right]^3=8 \cdot x\)
Karnataka CET-2017
Sets, Relation and Function
117250
If \(f: R \rightarrow R\) is defined by \(f(x)=\frac{x}{x^2+1}\) find \(\mathbf{f}(\mathbf{f}(2))\).
1 \(\frac{10}{29}\)
2 29
3 \(\frac{1}{29}\)
4 \(\frac{29}{10}\)
Explanation:
A It \(f: R \rightarrow R\) is defined by \(f(\mathrm{x})=\frac{\mathrm{x}}{\mathrm{x}^2+1}\) \(\therefore \quad f(2)=\frac{2}{2^2+1}=\frac{2}{5}\) \(\therefore \quad f(f(2))=f\left(\frac{2}{5}\right)=\frac{2 / 5}{\frac{4}{25}+1}\) \(=\frac{2 / 5}{29 / 25}=\frac{2}{5} \times \frac{25}{29}=\frac{10}{29}\)
117249
If \(f(x)=8 x^3, g(x)=x^{1 / 3}\), then fog(x) is
1 \(8^3 x\)
2 \(8 x^3\)
3 \(8 \mathrm{x}\)
4 \((8 x)^{1 / 3}\)
Explanation:
C Given \(f(\mathrm{x})=8 \mathrm{x}^3\), \(g(x)=x^{1 / 3}\) The fog \((\mathrm{x})=f(\mathrm{~g}(\mathrm{x}))\) \(=8 \cdot\left[\mathrm{x}^{1 / 3}\right]^3=8 \cdot x\)
Karnataka CET-2017
Sets, Relation and Function
117250
If \(f: R \rightarrow R\) is defined by \(f(x)=\frac{x}{x^2+1}\) find \(\mathbf{f}(\mathbf{f}(2))\).
1 \(\frac{10}{29}\)
2 29
3 \(\frac{1}{29}\)
4 \(\frac{29}{10}\)
Explanation:
A It \(f: R \rightarrow R\) is defined by \(f(\mathrm{x})=\frac{\mathrm{x}}{\mathrm{x}^2+1}\) \(\therefore \quad f(2)=\frac{2}{2^2+1}=\frac{2}{5}\) \(\therefore \quad f(f(2))=f\left(\frac{2}{5}\right)=\frac{2 / 5}{\frac{4}{25}+1}\) \(=\frac{2 / 5}{29 / 25}=\frac{2}{5} \times \frac{25}{29}=\frac{10}{29}\)
117249
If \(f(x)=8 x^3, g(x)=x^{1 / 3}\), then fog(x) is
1 \(8^3 x\)
2 \(8 x^3\)
3 \(8 \mathrm{x}\)
4 \((8 x)^{1 / 3}\)
Explanation:
C Given \(f(\mathrm{x})=8 \mathrm{x}^3\), \(g(x)=x^{1 / 3}\) The fog \((\mathrm{x})=f(\mathrm{~g}(\mathrm{x}))\) \(=8 \cdot\left[\mathrm{x}^{1 / 3}\right]^3=8 \cdot x\)
Karnataka CET-2017
Sets, Relation and Function
117250
If \(f: R \rightarrow R\) is defined by \(f(x)=\frac{x}{x^2+1}\) find \(\mathbf{f}(\mathbf{f}(2))\).
1 \(\frac{10}{29}\)
2 29
3 \(\frac{1}{29}\)
4 \(\frac{29}{10}\)
Explanation:
A It \(f: R \rightarrow R\) is defined by \(f(\mathrm{x})=\frac{\mathrm{x}}{\mathrm{x}^2+1}\) \(\therefore \quad f(2)=\frac{2}{2^2+1}=\frac{2}{5}\) \(\therefore \quad f(f(2))=f\left(\frac{2}{5}\right)=\frac{2 / 5}{\frac{4}{25}+1}\) \(=\frac{2 / 5}{29 / 25}=\frac{2}{5} \times \frac{25}{29}=\frac{10}{29}\)