What is the range of the function ?

Question

#y=(4x-3)/(2x)#

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Answer 1 · 2017-12-28T00:16:41

#(-oo, 2) uu (2, oo)#

Given:

#y = (4x-3)/(2x)= 2-3/(2x)#

Then:

#3/(2x)=2-y#

So taking the reciprocal of both sides:

#2/3x = 1/(2-y)#

Multiplying both sides by #3/2#, this becomes:

#x = 3/(2(2-y))#

So for any #y# apart from #2#, we can substitute #y# into this formula to give us a value of #x# that satisfies:

#y = (4x-2)/(2x)#

So the range is the whole of the real numbers except #2#, i.e. it is:

#(-oo, 2) uu (2, oo)#

graph{y = (4x-3)/(2x) [-10, 10, -5, 5]}