If the function $f (x) = \frac{3 x - c}{a x + 2}$ $f(x) = (3x-c)/(ax+2)$ is a constant function, what is the value of $a \cdot c$ $a*c$ ?

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Answer 1 · 2016-07-12T09:21:51

$a c = - 6$ $ac=-6$

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

So

$f (0) = f (1)$ $f(0) = f(1)$

$\Rightarrow \frac{3 \cdot 0 - c}{a \cdot 0 + 2} = \frac{3 \cdot 1 - c}{a \cdot 1 + 2}$ $=>(3*0-c)/(a*0+2)=(3*1-c)/(a*1+2)$

$- c (a + 2) = 2 \cdot (3 - c)$ $-c(a+2)=2*(3-c)$

$\Rightarrow - a c - 2 c = 6 - 2 c$ $=>-ac-2c=6-2c$

$\Rightarrow a c = - 6$ $=>ac=-6$

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

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