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How do you find the range of f(x) = x/x-2 where x>2?

BrainJuice

Please can you help.

Reply 1

B_9710

It may be helpful to express function as 1+2/(x/2). Now just find max and min value of function.

Reply 2

Towcestermaths

Original post by BrainJuice

Please can you help.

Consider the extreme values of x. AT the bottom end, when x is only very marginally greater than 2, the numerator will be approximately 2 and the denominator will be a very small number. Thus the function will be very large. As the value of x approaches 2, the value of the function will approach infinity. At the other end, as x becomes extremely large, the numerator will be approximately the same as the denominator and therefore the function will approach (but never reach) 1. So the range of f(x) will be f(x)>1