question_answer

Let \[f\,(x)=lo{{g}_{0.5}}\,({{x}^{2}}-5x+6),\] then \[f\,(x)\] is:

A) one - one but not onto

B) one - one and onto

C) onto but not one - one

D) neither one - one nor onto

Correct Answer: C

Solution :

\[\because \]\[f\,(x)={{\log }_{0.5}}\,({{x}^{2}}-5x+6)\]\[\Rightarrow \]f(x) will be defined if \[{{x}^{2}}-5x+6>0\]\[\Rightarrow \]\[(x-2)\,\,(x-3)>0\]

from graph of f(x) we can say that it will be a many-one and onto function.