Consider that the functions are given as,
[tex]\begin{gathered} f(x)=x+1 \\ g(x)=\frac{1}{x} \end{gathered}[/tex]Note that the composition function exists only if both the functions are defined at that point.
Note that the function g(x) is not defined at x=0.
Solve for the composite function as,
[tex]\text{fog(x)}=f(g(x))=f(\frac{1}{x})=\frac{1}{x}+1[/tex]The composite function contains the term 1/x which cannot be zero for any real value of 'x'.
So it follows that the composite function can never take the value 1,
[tex]\text{fog(x)}\ne1[/tex]Thus, the range of the composite function should be the set of all possible real numbers except 1.
