$\mathrm{f}:x\mapsto \cos x,x\in \mathbb{R},0\le x

Question

$\mathrm{f}:x\mapsto \cos x,x\in \mathbb{R},0\le x<\frac{\pi }{2}$ and $\mathrm{g}:x\mapsto \ln \left( {{x}^{2}} \right),x\in \mathbb{R},x\ne 0$. Determine, with reasons, whether $\text{fg}$ and $\text{gf}$ exist. If the composite function exists, give the rule, domain and range in exact form.

Accepted Answer

$\text{gf}$ exists. $\text{gf}\left( x \right)=\ln \left( {{\cos }^{2}}x \right),{{D}_{\text{gf}}}=[0,\frac{\pi }{2}),{{R}_{fg}}=(-\infty ,0]$

Functions - Range of a Composite Function

Functions - Range of a Composite Function

Video Solution:

Solution:

Solution locked