f(x) = 4x - m, g(x) = mx + 11, fg(x) = 8x + n. m and n are constants. Find the value of n.

If f(x) = 4x - m, and g(x) = mx +11, then the combined functions are: fg(x) = 4(mx +11) -m, or expanded to fg(x) = 4mx + 44 - m.

We are told that this function of 'f' and 'g' can also be written as fg(x) = 8x + n. This means that 8x = 4mx, as '4m' is the only co-efficient of x in the combined 'fg(x)' function. This simplifies to 8 = 4m, then further to 2 = m.

To find the value of 'n' we need to create a different equation. n = 44 - m, as this is what is left of the combined 'fg(x)' function, once the coefficient of x has been found, so must form the 'n' part of the original 'fg(x)' function.

We can sub in 'm', which we know is 2, so n = 44 -2, which simplifies to n = 42.

Therefore, our final answer is n = 42.