question_answer

Let \[f(x)=\frac{2}{x+1},\,\,g(x)=\cos x\] and \[h(x)=\sqrt{x+3}\] then the if range of the composite function fogoh, is

A) \[{{R}^{+}}\]                                 

B) \[R-\{0\}\]

C) \[[1,\,\,\infty )\]            

D) \[{{R}^{+}}-\{1\}\]

Correct Answer: C

Solution :

 Let \[f\] image of \[goh\] image,\[fogoh=F(x)=f[goh(x)]\] \[F(x)=\frac{2}{\cos \sqrt{x+3}+1}\] Now\[x+3\ge 0\]and\[-1<\cos \sqrt{x+3}\le 1\] \[\sqrt{x+3}\ne (2n-1)\pi ,\,\,n\in N\]