Using the figure below, estimate the following?

enter image source here (a) f(g(2))=
(b) g(f(2))=
(c) f(f(3))=
(d) g(g(3))=

I'm not exactly sure how to the values using this graph?

1 Answer
Nov 13, 2017

a) f(g(2))~~4
b) g(f(2))~~1.25
c) f(f(3))~~3.6
d) g(g(3))~~2.25

Explanation:

For each of these, start from the innermost portion, find the value shown as the x value on the x-axis, and read upwards until you hit the function shown. Note that each block in the graph looks to be 0.5, so half of a block would be about 0.25.

f(g(2))

For this, start on the inside with g(2). Use the graph of g(x) to estimate the value g(2). Finding x =2, and looking upwards to g(x), it looks as though g(2) is about 1.6. Now, find x = 1.6 and look upwards to f(x) to find what f(1.6) looks to be, roughly. It looks like f(1.6) ~~ 4.

g(f(2))

First, approximate f(2) using the graph. It looks like f(2) ~~ 3.25. Now, use the graph of g(x) to approximate g(3.25). It looks like g(3.25)~~1.25.

f(f(3))

Start by using the graph to estimate f(3). In this case, f(3) looks to be about 1.75. Substituting this, we can now estimate f(1.75) from the graph, which gives us f(1.75)~~3.6

g(g(3))

Start by using the graph to estimate g(3). In this case, g(3) looks to be about 1.25. Now, substitute and estimate what g(1.25) is from the graph. It looks like g(1.25)~~2.25