Question

2. What is the range of the function f(x)=|x-1|/(x-1)
​

Answer 1

Answer:

Before finding its range, we should first go for it domain as outcomes always depend on inputs(atleast in mathematics). This is function is defined for all real nos. Except 1 as it would make denominator zero which makes no sense.

Since its a modulus function we need to break it in simpler functions by breaking modulus function.

F(x) = (x-1)/(x-1) x>1 and you can see both numerator and denominator are same for every x therefore F(x) =1 for all x>1

Similarly F(x) = -1 for all x<1

F(x) : (all real nos.) -( 1) to {-1,1}