Chapter 3.2, Problem 88E

(a)

To determine

To match: The each functions with its given graph.

Answer to Problem 88E

Graph n is match with $f\left(x\right)=3^x$

And graph m is matched with $g\left(x\right)={\log }_{3}x$

Explanation of Solution

Given:

It is given that the graph of $f\left(x\right)=3^x\text{and}g\left(x\right)={\log }_{3}x$

Note: the graphs are labelled as m and n.

  

Consider the graph which is shown below, it is clear that m is related to $f\left(x\right)=3^x$

And also n is related to $g\left(x\right)={\log }_{3}x$ .

  

(b)

To determine

The value of function g(b).

Answer to Problem 88E

The value of the function:

  $g\left(b\right)=a$

Explanation of Solution

Given:

It is given that function f(a) =b.

Since f(a) = b

Therefore $3^a=b$

Now changing the exponential form to the logarithmic form

  $a=g\left(b\right)$

Hence, $g\left(b\right)=a$