Preview Activity 3.4.1.
(a)
Complete the followion table to generate certain values of \(P\text{.}\)
| \(t\) | -3 | -2 | -1 | 0 | 1 | 2 | 3 |
| \(y = P(t) = 10^t\) |
(b)
Why does \(P\) have an inverse function?
(c)
Since \(P\) has an inverse function, we know there exists some other function, say \(L\text{,}\) such that writing “\(y = P(t)\)” says the exact same thing as writing “\(t = L(y)\)”. In words, where \(P\) produces the result of raising \(10\) to a given power, the function \(L\) reverses this process and instead tells us the power to which we need to raise \(10\text{,}\) given a desired result. Complete the followin table to generate a collection of values of \(L\text{.}\)
| \(y\) | \(10^{-3}\) | \(10^{-2}\) | \(10^{-1}\) | \(10^{0}\) | \(10^{1}\) | \(10^{2}\) | \(10^{3}\) |
| \(L(y)\) |
(d)
What are the domain and range of the function \(P\text{?}\) What are the domain and range of the function \(L\text{?}\)
