Here we will explore some properties of inverse functions. (a) The function f (x) = 4x − 3 is invertible. Find the inverse functionf^−1 (x) and plot a graph of both f and f^−1. (b) The function f(x) = x2 is not invertible. Try to solve for the inverse anyway, and sketch graphs of f and everything you get by trying to solve for the inverse (c) What do we notice about these graphs? In particular, what is strange about the graph(s) for f−1 when f was not invertible? Think about a test we have for determining if a graph is represented by a function. (d) Look at the graphs you have above and see if you can find a relation between the graph of f and the grapg of f^−1. from a more algebraic perspective, if the point (a,b) is on the graph of f, what point has to be on the graph of f−1? What does this mean in terms of the geometry of the graphs? (e) With this relation you described in the previous part, how does the function test for f−1 relate to a different type of test on the graph of f? That is, is there a test we could perform on the graph of f to see if it will be invertible?
Here we will explore some properties of inverse functions.
(a) The function f (x) = 4x − 3 is invertible. Find the inverse functionf^−1 (x) and plot a graph of both f and f^−1.
(b) The function f(x) = x2 is not invertible. Try to solve for the inverse anyway, and sketch graphs of f and everything you get by trying to solve for the inverse
(c) What do we notice about these graphs? In particular, what is strange about the graph(s) for f−1 when f was not invertible? Think about a test we have for determining if a graph is represented by a function.
(d) Look at the graphs you have above and see if you can find a relation between the graph of f and the grapg of f^−1. from a more algebraic perspective, if the point (a,b) is on the graph of f, what point has to be on the graph of f−1? What does this mean in terms of the geometry of the graphs?
(e) With this relation you described in the previous part, how does the function test for f−1 relate to a different type of test on the graph of f? That is, is there a test we could perform on the graph of f to see if it will be invertible?
Trending now
This is a popular solution!
Step by step
Solved in 7 steps with 7 images
