question_answer

Let \[f(x)={{\log }_{0.5}}({{x}^{2}}-5x+6),\] 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.