Question

Can somebody please show me how to do this problem

Answer 1

Answer:

• g(20) > f(20)
• g(x) exceeds f(x) for any x > 4

Step-by-step explanation:

As with most graphing problems not involving straight lines, it works well to start with a table of values. Pick a few values of x and compute f(x) and g(x) for those values. Plot the points and draw a smooth curve through them.

As in the attached, your table will show that there are two points of intersection between f(x) and g(x), and that for values of x more than 4, g(x) becomes much greater very quickly. Both curves rapidly reach the top of your graph space.

To find whether f(20) or g(20) is greater, you can evaluate the functions for that value of x.

  f(20) = 20² = 400

  g(20) = 2²⁰ = 1,048,576

Clearly, g(20) has a greater value.