The inverse of a function is a new function that reverses the original function's input and output. In other words, if the original function takes an input x and produces an output y, the inverse function takes y as an input and produces x as an output.
To find the inverse of a function, you can follow these steps:
The inverse of g(x) = x/3 - 5 is g-1(x) = 3x + 15. To find the inverse, we follow the steps outlined in the previous answer.
To check if a function and its inverse are correct, you can use the composition method. This involves plugging the inverse function into the original function and vice versa. If the output of the composition is x for both cases, then the functions are inverses of each other.
No, not every function has an inverse. A function must be one-to-one (each input has a unique output) and onto (every output has at least one corresponding input) to have an inverse. If a function fails either of these criteria, it does not have an inverse.