Question

If the function `f(x) = (3x-c)/(ax+2)` is a constant function, what is the value of `a*c` ?

Answer 1

`ac=-6`

Explanation:

`f(x)` being a constant function it will have same value for all real values of x.

So

`f(0) = f(1)`

`=>(3*0-c)/(a*0+2)=(3*1-c)/(a*1+2)`

`-c(a+2)=2*(3-c)`

`=>-ac-2c=6-2c`

`=>ac=-6`

Otherwise differentiating the function `f(x)` w.r.to x and equating `f'(x)=0` we can get the same result.