Question

1. Consider the functions f(x)=1/(x)+4 and g(x)=2/(x). Graph f and g on the same grid.

a) Determine the points of intersection of the two functions.
b) Show where f(x)<g(x).
c) Solve the equation 1/(x)+4=2(x) to check your answer to part a).
d) Solve the inequality 1/(x)+4<2/(x) to check your answer to part b)

Answer 1

Sorry but i forgot to pose what subject it was.

Answer 2

consider the graph of y = 1/x
I assume you know what it looks like.

f(x) = y+4, so it is the same curve shifted up by 4

g(x) = 2y, so it is the same curve scaled vertically by a factor of 2.

Visit

http://rechneronline.de/function-graphs/

and enter the functions. All will become clear. You might want to adjust the range to be -10 : 10, and plot a 3rd curve,

1/x+4 - 2/x

so you can see where f-g = 0.