kris2fer said:Homework Statement
Given f(x) = x2+3x+2, what is f-1(f(x))?
Homework Equations
The Attempt at a Solution
Algebraically, getting f-1(x) is as follows:
y=x2+3x+2
x=y2+3x+2
y=+/-√(x+0.25)-1.5
f-1(x)=+/-√(x+0.25)-1.5
f-1(f(x))=+/-√(x2+3x+2+0.25)-1.5
f-1(f(x))=+/-√(x+1.5)2-1.5
f-1(f(x))=x or -x-3
I thought f-1(f(x)) was always x. What's wrong with -x-3?
Dick said:Yes, it's always x. Your function doesn't even have an inverse, it's not 1-1. As the +/- is telling you. That's what's going wrong.
An inverse function is a function that undoes the action of another function. In other words, if we apply a function f to an input x, the inverse function f-1 will take the output of f and return the original input x.
To find the inverse of a function, we follow the steps:
A one-to-one function is a function in which each input has a unique output, while a many-to-one function is a function in which multiple inputs may have the same output. The inverse of a one-to-one function is also a function, while the inverse of a many-to-one function is not.
The notation f-1(f(x)) represents the composition of a function f and its inverse f-1. This notation is significant because it shows that the output of the function f is being used as the input for its inverse, resulting in the original input being returned.
To graph the inverse of a function, we can use the points on the original function's graph by switching the x and y coordinates. We can also use the steps mentioned earlier to find the inverse function and then plot the points to create its graph.