Question

Using the figure below, estimate the following?

(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?

Answer 1

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`