Functions

Given that f(x) = 4x + k , and g(x) = x - 2 , find the possible value of m and k if  f[g(x)] = mx + 8

I'm assuming that these represent linear equations  with m = slope and k  = y intercept

f (g (x) )  =   4 (x - 2)  +  k  

So.....

4(x - 2) +  k  =  mx +  8     

4x  -  8  + k  =  mx  +  8            let k  =  16

4x  + 8  =  mx  + 8         ⇒      m   =  4

So

m  =  4     and  k   =  16

If  -8  +  k  is the y intercept of one line  and  8 is the y intercept of the other....and we want the y intercepts to be the same, we have that

-8  +  k  =  8      add 8 to both sides

k   =  16