question_answer

The function\[f(x)=2-3x\]is:

A)  increasing            

B)         decreasing

C)  neither decreasing nor increasing

D)  none of the above

Correct Answer: B

Solution :

Key Idea: If \[f(x)\] is a function, it will be increasing or decreasing if \[f(x)>0\]or \[f(x)<0.\] We have\[f(x)=2-3x\] On differentiating w.r.t. \[x,\] we get \[f(x)=-3<0\] \[\therefore \] Function is decreasing for every value of \[x.\] Alternate Solution: Let \[y=f(x)=2-3x\] \[\Rightarrow \]    \[y+3x=2\,\] \[\Rightarrow \]    \[\frac{x}{2/3}+\frac{y}{2}=1\] It is clear from the figure that for increasing the value of \[x\] from \[-\infty \]to \[\infty ,\]we will get the decreasing value of\[y\] from \[\infty \]to \[-\infty \]. \[\therefore \] It is decreasing function.