Consider the functions *f *and *g *defined by

f(x)=sqrt((x+1)/(x-1))

and

g(x)=(sqrt x+1)/(sqrt x-1)

explain why f and g are not the same function.

Thanks!

WhichWitchIsWhich
Nov 1, 2017

#1**+1 **

The first function is defined on (-inf, -1] U (1, inf )

However.........the second function is only defined for (1, inf )

Note that if let x = -2, the first function is

sqrt ( [-2 + 1 ] / [ -2 -1] ) = sqrt ( -1 / -3 ) = sqrt (1/3)

But....in the second function we have

sqrt [ -2 + 1 ] / sqrt [ -2 - 1 ] = sqrt [ -1] / sqrt [ -3] and the numerator/denominator are both non-real

CPhill
Nov 1, 2017