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

Answer:

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#