Login/Sign Up
Find gof and fog when f: R → R and g : R → R is defined by \[\mathbf{f}\left( \mathbf{x} \right)\text{ }=~{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}~-\text{ }\mathbf{3}\] and \[\mathbf{g}\left( \mathbf{x} \right)\text{ }=\text{ }\mathbf{3x}~-\text{ }\mathbf{4}~\]
Find gof and fog when f: R → R and g : R → R is defined by \[\mathbf{f}\left( \mathbf{x} \right)\text{ }=~{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}~-\text{ }\mathbf{3}\] and \[\mathbf{g}\left( \mathbf{x} \right)\text{ }=\text{ }\mathbf{3x}~-\text{ }\mathbf{4}~\]
CBSE | Class 12 | Exercise 2.2 | Function | Maths | RD Sharma
Find gof and fog when f: R → R and g : R → R is defined by \[\mathbf{f}\left( \mathbf{x} \right)\text{ }=~{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{2x}~-\text{ }\mathbf{3}\] and \[\mathbf{g}\left( \mathbf{x} \right)\text{ }=\text{ }\mathbf{3x}~-\text{ }\mathbf{4}~\]

Given, f: R → R and g: R → R

So, gof: R → R and fog: R → R

\[f\left( x \right)\text{ }=~{{x}^{2}}~+\text{ }2x~-\text{ }3\] and \[g\left( x \right)\text{ }=\text{ }3x~-\text{ }4\]

(gof) (x) = g (f(x))

\[=~g~({{x}^{2~}}+\text{ }2x\text{ }-\text{ }3)\]

\[=~3~({{x}^{2~}}+\text{ }2x\text{ }-\text{ }3)~-\text{ }4\]

\[=~3{{x}^{2~}}+~6x~-~9~-~4\]

\[=~3{{x}^{2~}}+\text{ }6x\text{ }-\text{ }13\]

Now, (fog) (x) = f (g (x))

\[=~f~\left( 3x\text{ }-\text{ }4 \right)\]

\[=~{{\left( 3x~-~4 \right)}^{2~}}+\text{ }2~\left( 3x~-~4 \right)~-3\]

\[=~9{{x}^{2~}}+\text{ }16\text{ }-\text{ }24x\text{ }+\text{ }6x\text{ }\text{ }8\text{ }-\text{ }3\]

\[=~9{{x}^{2~}}-\text{ }18x~+~5\]

i

More Material