Question

Let f(x) =x+1 and g(x)=1/x. The graph of (f o g)(x) is shown below. What is the range of (f o g)(x)?

Answer 1

Looks like all real numbers except 1. It touch's all the y except 1 aka range

Answer 2

all real numbers except y=1

Explanation:

`f(x)=x+1`

`g(x)=(1)/(x)`

`(f og)(x)= f(g(x))`

Plug in 1/x for g(x)

`(f og)(x)= f(g(x))=f((1)/(x))`

Now we plug in the fraction in f(x)

`(f og)(x)= f(g(x))=f((1)/(x))=(1)/(x)+1`

Range of the function are the y values for which the function is defined

In the graph , we can see that the graph goes close to y=1 but does not cross y=1

So range is all real numbers except y=1