Question

1. the function c = f(p) represents the cost, c, to get p photos printed. interpret the meaning of the statement f^(-1)(15)=45.
2. let q = f(p) represent the indoor air quality as a function of the number of house plants, p, that are in a home. explain what information is given by the function f^(-1). be sure to include both the input and the output in your explanation.
3. a table of selected values is given for a one - to - one function, p(x). what is p^(-1)(5)?

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$$\begin{array}{c|cccccc}x&-5&-3&0&1&3&5\\hline p(x)&12&5&2&0& - 1&3\\end{array}$$

Explanation:

1.

Step1: Recall inverse - function concept

The function $c = f(p)$ gives cost $c$ for $p$ photos. The inverse function $f^{-1}(c)=p$.

Step2: Interpret the given statement

Given $f^{-1}(15) = 45$, it means that when the cost $c = 15$, the number of photos $p = 45$. That is, it costs 15 units of currency to print 45 photos.

Step1: Recall inverse - function concept

The function $q = f(p)$ gives indoor air quality $q$ as a function of the number of house - plants $p$. The inverse function $f^{-1}(q)=p$.

Step2: Explain the inverse function

The input of the inverse function $f^{-1}$ is the indoor air quality $q$, and the output is the number of house - plants $p$. So, $f^{-1}(q)$ gives the number of house - plants $p$ required to achieve an indoor air quality of $q$.

Step1: Recall inverse - function property

For a one - to - one function $y = p(x)$ and its inverse $x = p^{-1}(y)$, if $p(a)=b$, then $p^{-1}(b)=a$.

Step2: Find the value in the table

We are looking for $x$ such that $p(x)=5$. From the table, when $x=-3$, $p(-3)=5$. So, $p^{-1}(5)=-3$.

Answer:

It costs 15 units of currency to print 45 photos.

2.