Question

The range of the function f:R-{3}-R defined by f(x)=|x-3|÷(x-3) is:
a) {0,1}
b){1,-1}
c){3,-3}
d){-1,0}

Answer 1

Range = { 1, -1}

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Answer 2

➡HERE IS YOUR ANSWER⬇

Given that :

f : |R - {3} --> |R

f(x) = |x-3| ÷ (x-3)

----------------------

|x-3| = (x-3), when x > 3

|x-3| = -(x-3), when x < 3

-----------------------------------

Now,

when x > 3,

f(x) = (x-3)÷(x-3) = 1

and

when x < 3,

f(x) =- (x-3)÷ (x-3) = -1

Therefore, the range of f is {1, -1}.

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