EXERCISE SOLUTION-0.4, Pag#48, Calculus Book

Q.01 Determine whether $f$ and $g$ are inverse functions. Solution: (a) $$\begin{aligned} & f(x)=4 x, \quad g(x)=\frac{1}{4} x \\ \\ & f(g(x))=4 g(x)=4 \cdot \frac{1}{4} x=x \\ \\ & g(f(x))=\frac{1}{4} f(x)=\frac{1}{4} \cdot 4 x=x \\ \\ & \Rightarrow \quad f(g(x))=x, g(f(x))=x \end{aligned}$$ $\Rightarrow \quad f$ and $g$ are inverse functions. (b) $$\begin{aligned} f(x)=3 x+1, \quad … Read more