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Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions

Class 12 Maths · Relations And Functions · Mcq Single Correct #47

Let \(m,n\in\mathbb{R}\), \(m\ne n\). Define \(f:\mathbb{R}\setminus\{n\}\to\mathbb{R}\) by \(f(x)=\frac{x-m}{x-n}\). Then

✅ Step-by-Step Solution

Final Answer: Option (B): f is one-one into
  1. For allowed inputs, \(f(x)=f(y)\) gives \((m-n)(x-y)=0\), so \(x=y\). Also \(f(x)=1\) would imply \(m=n\), which is excluded. Every real \(t\ne1\) has preimage \(x=(tn-m)/(t-1)\), and this is not \(n\). Thus the function is one-one with range \(\mathbb{R}\setminus\{1\}\), so it is into.

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