# If f(x)=mx-2 , g(x)=(3x+2n)/6 and (g@f)(x) is a unit function, what is m+n ?

Jul 14, 2016

$m = 0 , n = 6 \to m + n = 6$

#### Explanation:

Supposing that $g \circ f$ to be a unit function is

$\left(g \circ f\right) \left(x\right) = 1 \forall x \in \mathbb{R}$

$\left(g \circ f\right) \left(x\right) = \frac{3 f \left(x\right) + 2 n}{6} = \frac{1}{6} \left(2 n + 3 \left(m x - 2\right)\right)$

or

$\left(g \circ f\right) \left(x\right) = \frac{m}{2} x + \frac{n}{3} - 1 = 1$

then

$m = 0 , n = 6$

then $m + n = 6$