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.You need to login to perform this action.
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