Let be defined by and be defined by

MATHEMATICS · Multi-part · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Let f:(0,∞)→Rf:(0,\infty)\to\mathbb R be defined by f(x)=ln⁡xf(x)=\ln x and g:R→(0,∞)g:\mathbb R\to(0,\infty) be defined by g(x)=exg(x)=e^{x}. Show that ff and gg are inverses of each other. (i) Evaluate (f∘g)(x)(f\circ g)(x) for a general x∈Rx\in\mathbb R. (ii) Evaluate (g∘f)(x)(g\circ f)(x) for a general x∈(0,∞)x\in(0,\infty). (iii) What can you conclude about ff and gg?

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