+267 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!
+129852 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
