Let f:R-(-1)/(2) R and g:R-(-5)/(2) R be defined as f(x)=(2x+3)/(2x+1) and g(x)=(|x|+1)/(2…

Question

Let $f:R-{\frac{-1}{2}}	o R$ and $g:R-{\frac{-5}{2}}	o R$ be defined as $f(x)=\frac{2x+3}{2x+1}$ and $g(x)=\frac{|x|+1}{2x+5}$. Then, the domain of the function fog is :

Accepted Answer

$\begin{gathered} f(x)=\frac{2x+3}{2x+1};x
e -\frac{1}{2} \ g(x)=\frac{|x|+1}{2x+5},x
e -\frac{5}{2} \end{gathered}$

Domain of $f(g(x))$

$f(g(x))=\frac{2g(x)+3}{2g(x)+1}$

$x
e -\frac{5}{2}$ and $\frac{|x|+1}{2x+5}
e -\frac{1}{2}$

$x\in R-{-\frac{5}{2}}$ and $x\in R$

$	herefore $ Domain will be $R-{-\frac{5}{2}}$

Solutions · 1