if f(x)=4x^2 and g(x)=5 what is g(f (2x) ) ?

  g(f(2x)) = 5

Step-by-step explanation:

The equation g(x) = 5 tells you the value of x is immaterial. You can make the argument as complicated as you like, and the result is still 5.

18

step-by-step explanation:

draw the shape and you will see that f and k are actually at adjacent vertices (points of the hexagon that are neighboring).   so find the distance between (1,2) and (4,2).   that is easy since (1,2) and (4,2) is just a vertical distance to count, which is 3.   it is a regular polygon which means all sides are congruent.   you have 6 sides (hexa) so multiply 6 by 3 to receive 18.

answer: yes, since the line has a steeper rate of change than the exponential the y-values will be greater and they will only intersect one time.