)caitlinbennet said:
tiny-tim said:hi caitlinbennet! welcome to pf!
(try using the X2 button just above the Reply box
so f(x) = … ?
and what does that tell you about s-1 ?
(1+s(x))/1-s(x)?tiny-tim said:
caitlinbennet said:
tiny-tim said:f-1(f(y)) = … ?
The inverse of a function is a function that "undoes" what the original function does. It is represented by swapping the x and y variables and solving for y. In this case, the inverse of s(x) is given by the formula s-1(x) = [1+f(x)]/[1-f(x)].
To find the inverse of a function, swap the x and y variables and solve for y. This can be done by using algebraic methods such as isolating y on one side of the equation or using the concept of inverse operations.
Not all functions have an inverse. A function must be one-to-one, meaning that each input (x) corresponds to a unique output (y), in order for its inverse to exist. In this case, the function s(x) meets this criterion, so it does have an inverse.
The inverse of a function is typically represented by adding a "-1" superscript to the original function's name, such as s-1(x) in the case of the function s(x). It is also common to see the inverse written as f-1(x) or g-1(x).
The inverse of a function and the original function are reflections of each other across the line y=x. This means that the input and output values are switched, and the graph of the inverse is a reflection of the original function's graph across this line.