Question

Let f(x) = x + 1 and g(x) = . The graph of (fog)(x) is shown below.6 54221 +-54-3-2-12 3 4 5XWhat is the range of (fog)(x)?

Answer 1

Consider that the functions are given as,

`\begin{gathered} f(x)=x+1 \\ g(x)=(1)/(x) \end{gathered}`

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,

`\text{fog(x)}=f(g(x))=f((1)/(x))=(1)/(x)+1`

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,

`\text{fog(x)}\\e1`

Thus, the range of the composite function should be the set of all possible real numbers except 1.