117243
Let \(f\) be a non-zero real valued continuous function satisfying \(f(x+y)=f(x)\). \(f(y)\) for all \(x, y\) \(\in\). If \(f(2)=9\), then \(f(6)\) is equal to
117245
Let \(R\) be the set of real numbers and the mapping \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)=5-x^2\) and \(g(x)=3 x-4\), then the value of (fog)(-1) is
1 -44
2 -54
3 -32
4 -64
Explanation:
A Given, \(f(x)=5-x^2 \text { and } g(x)=3 x-4\) \(\therefore \quad \text { fog }(\mathrm{x})=\mathrm{f}(\mathrm{g}(\mathrm{x}))\) \(=5-(3 \mathrm{x}-4)^2\) \(=5-\left[9 x^2+16-24 x\right]\) \(=5-9 \mathrm{x}^2-16+24 \mathrm{x}\) \(=-9 \mathrm{x}^2+24 \mathrm{x}-11\) \(\therefore \quad \text { fog }(-1)=-9(1)+24(-1)-11\) \(=-9-24-11=-44\)
WB JEE-2010
Sets, Relation and Function
117246
Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)\) \(=2 x+1 \& g(x)=x^2-2\) determine (gof) \((x)=\)
117243
Let \(f\) be a non-zero real valued continuous function satisfying \(f(x+y)=f(x)\). \(f(y)\) for all \(x, y\) \(\in\). If \(f(2)=9\), then \(f(6)\) is equal to
117245
Let \(R\) be the set of real numbers and the mapping \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)=5-x^2\) and \(g(x)=3 x-4\), then the value of (fog)(-1) is
1 -44
2 -54
3 -32
4 -64
Explanation:
A Given, \(f(x)=5-x^2 \text { and } g(x)=3 x-4\) \(\therefore \quad \text { fog }(\mathrm{x})=\mathrm{f}(\mathrm{g}(\mathrm{x}))\) \(=5-(3 \mathrm{x}-4)^2\) \(=5-\left[9 x^2+16-24 x\right]\) \(=5-9 \mathrm{x}^2-16+24 \mathrm{x}\) \(=-9 \mathrm{x}^2+24 \mathrm{x}-11\) \(\therefore \quad \text { fog }(-1)=-9(1)+24(-1)-11\) \(=-9-24-11=-44\)
WB JEE-2010
Sets, Relation and Function
117246
Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)\) \(=2 x+1 \& g(x)=x^2-2\) determine (gof) \((x)=\)
117243
Let \(f\) be a non-zero real valued continuous function satisfying \(f(x+y)=f(x)\). \(f(y)\) for all \(x, y\) \(\in\). If \(f(2)=9\), then \(f(6)\) is equal to
117245
Let \(R\) be the set of real numbers and the mapping \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)=5-x^2\) and \(g(x)=3 x-4\), then the value of (fog)(-1) is
1 -44
2 -54
3 -32
4 -64
Explanation:
A Given, \(f(x)=5-x^2 \text { and } g(x)=3 x-4\) \(\therefore \quad \text { fog }(\mathrm{x})=\mathrm{f}(\mathrm{g}(\mathrm{x}))\) \(=5-(3 \mathrm{x}-4)^2\) \(=5-\left[9 x^2+16-24 x\right]\) \(=5-9 \mathrm{x}^2-16+24 \mathrm{x}\) \(=-9 \mathrm{x}^2+24 \mathrm{x}-11\) \(\therefore \quad \text { fog }(-1)=-9(1)+24(-1)-11\) \(=-9-24-11=-44\)
WB JEE-2010
Sets, Relation and Function
117246
Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)\) \(=2 x+1 \& g(x)=x^2-2\) determine (gof) \((x)=\)
117243
Let \(f\) be a non-zero real valued continuous function satisfying \(f(x+y)=f(x)\). \(f(y)\) for all \(x, y\) \(\in\). If \(f(2)=9\), then \(f(6)\) is equal to
117245
Let \(R\) be the set of real numbers and the mapping \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)=5-x^2\) and \(g(x)=3 x-4\), then the value of (fog)(-1) is
1 -44
2 -54
3 -32
4 -64
Explanation:
A Given, \(f(x)=5-x^2 \text { and } g(x)=3 x-4\) \(\therefore \quad \text { fog }(\mathrm{x})=\mathrm{f}(\mathrm{g}(\mathrm{x}))\) \(=5-(3 \mathrm{x}-4)^2\) \(=5-\left[9 x^2+16-24 x\right]\) \(=5-9 \mathrm{x}^2-16+24 \mathrm{x}\) \(=-9 \mathrm{x}^2+24 \mathrm{x}-11\) \(\therefore \quad \text { fog }(-1)=-9(1)+24(-1)-11\) \(=-9-24-11=-44\)
WB JEE-2010
Sets, Relation and Function
117246
Let \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined by \(f(x)\) \(=2 x+1 \& g(x)=x^2-2\) determine (gof) \((x)=\)
