Final answer:
To check if two functions are inverses, you can use function composition to see if they result in the identity function, or utilize a calculator like the TI-83 or TI-84 series to compute the inverse directly.
Step-by-step explanation:
To determine if two functions are inverses of each other, you can use a couple of methods.
- Function composition calculator: This involves taking the composition of the two functions (F and G, for example) and verifying if the composition results in the identity function. The step-by-step approach (Solution A), involves computing F(G(x)) and G(F(x)); if both compositions result in x, then F and G are inverses of each other.
- Inverse function calculator: The other method is to use the TI-83, TI-83+, or TI-84 calculators (Solution B) which have inbuilt functions to calculate the inverse of a given function directly.
Understanding the exponential function and its inverse, the natural log (ln), is useful in cases where you may need to use fundamental principles to find an inverse without a calculator. Similarly, knowing the relationship between a function and its inverse, like how the exponential function and natural log are inverses, is fundamental in mathematics.