Let $\mathrm{f}, \mathrm{g}: \mathbf{N} \rightarrow \mathbf{N}$ be defined by $\mathrm{f}(\mathrm{x}

Question

Let $\mathrm{f}, \mathrm{g}: \mathbf{N} \rightarrow \mathbf{N}$ be defined by $\mathrm{f}(\mathrm{x})=3 \mathrm{x}+5$ and $\mathrm{g}(\mathrm{x})=\mathrm{x}^2-\mathrm{x}$. Then the number of elements in $\{\mathrm{x}: \mathrm{f}(\mathrm{x})=\mathrm{g}(\mathrm{x})\}$ is

Professor PC Thomas Classes · Answer

$ \begin{aligned} & f(x)=g(x) \ & \Rightarrow \quad 3 x+5=x^2-x \ & \Rightarrow x^2-4 x-5=0 \ & \Rightarrow x=-1 	ext { or } 5 	ext { But } x \in N \quad 	herefore x=5 \end{aligned} $