# 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?

Nov 13, 2017

a) $f \left(g \left(2\right)\right) \approx 4$
b) $g \left(f \left(2\right)\right) \approx 1.25$
c) $f \left(f \left(3\right)\right) \approx 3.6$
d) $g \left(g \left(3\right)\right) \approx 2.25$

#### 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 $g \left(2\right)$. Use the graph of $g \left(x\right)$ to estimate the value $g \left(2\right)$. Finding $x = 2$, and looking upwards to $g \left(x\right)$, it looks as though $g \left(2\right)$ is about 1.6. Now, find $x = 1.6$ and look upwards to $f \left(x\right)$ to find what $f \left(1.6\right)$ looks to be, roughly. It looks like $f \left(1.6\right) \approx 4$.

g(f(2))

First, approximate $f \left(2\right)$ using the graph. It looks like $f \left(2\right) \approx 3.25$. Now, use the graph of $g \left(x\right)$ to approximate $g \left(3.25\right)$. It looks like $g \left(3.25\right) \approx 1.25$.

f(f(3))

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

g(g(3))

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