reversed functions
Composition
What if we were to compose these two functions? That is we make a new function
whereby we take a domain number for the exponential function, get the function
value, and then take this function value as the input into the logarithmic funciton,
and get is output.
Setup
We have two partnered exponential and logarithmic functions: and .
- (a)
- Let be a domain number of .
- (b)
- is in a pair: .
- (c)
- View as a number in the domain of .
- (d)
- We already know that is a pair in , because and are partnered. Their pairs are reversed.
- (e)
- That tells us that
was partnered with . then we reversed the pair and is partnered with .
The composition pairs with itself: for all of the domain numbers.
We have seen that and are two partnered exponential and logarithmic functions.
Map out the pairs for the composition, .
Let’s try it the other way.
We have seen that and are two partnered exponential and logarithmic functions.
Map out the pairs for the composition, .
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more examples can be found by following this link
More Examples of Percent Change