• # 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

 $\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.