There is a really fast way of finding the ranges of functions of the form f(x)=cx+dax+b where the f(x) is defined from R−{c−d} to R.
The range is simply R−{ca}. In other words, the range is R−{the coefficient of x in the denominatorthe coefficient of x in the numerator} [verify this!].
For example, the range of f(x)=5x+93x+2 is R−{53}.
Now consider the following statements.
[1]. The range of f(x)=4x+39x−5 is R−{49}.
[2]. The range of f(x)=91x−5626x−16 is R−{9126}.
[3]. The range of f(x)=17x−41−2x−6 is R−{17−2}.
Which of them are correct?
This problem is from the set "MCQ Is Not As Easy As 1-2-3". You can see the rest of the problems here.