Suppose the domain of f is (-1,1). Define the function g by g(x)=f(x+1).What is the domain of g?

Since the domain of  f(x)  is  -1 < x < 1  ,

 

Then the domain of  f(x + 1)  is  -1 < x + 1 < 1 .

 

-1 < x + 1 < 1   simplifies to

-2 < x < 0

 

So the domain of  f(x + 1)  is  (-2, 0) ,

 

And  g(x) = f(x + 1)  so the domain of  g(x)  is  (-2, 0) .