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Here is a set of practice problems to accompany the Inverse Functions section of the Graphing and Functions chapter of the notes for Paul Dawkins Algebra course at Lamar University.
10.3 Practice - Inverse Functions. State if the given functions are inverses. 1) g(x) = x5. − −. 3. f(x) = 5√. − −. x 3. 3) f(x) = −x −1.
Practice evaluating the inverse function of a function that is given either as a formula, or as a graph, or as a table of values.
Derivative of the inverse function at a point is the reciprocal of the derivative of the function at the corresponding point . Slope of the line tangent to 𝒇 at 𝒙= is the reciprocal of the slope of 𝒇 at 𝒙= .
Improve your understanding of inverse functions with practice questions. Master the concepts, solve problems, and enhance your mathematical proficiency effectively.
Inverse Functions – Example and Practice Problems. An inverse function is a function that will reverse the effect produced by the original function. These functions have the main characteristic that they are a reflection of the original function with respect to the line y = x.
1) Describe why the horizontal line test is an effective way to determine whether a function is one-to-one? 2) Why do we restrict the domain of the function \(f(x)=x^2\) to find the function’s inverse? 3) Can a function be its own inverse? Explain. 4) Are one-to-one functions either always increasing or always decreasing? Why or why not?
PRACTICE PROBLEMS OF FINDING INVERSE FUNCTIONS. For each of the following functions : Problem 1 : a) f (x) = 2x+5 Solution. b) f (x) = (3-2x)/4 Solution. c) f (x) = x+3 Solution. (i) Find f-1(x) Solution. (ii) sketch y = f (x), y = f-1(x) and y = x on the same axes. Solution.
Using composition of functions, show that f (x) = 2x - 3 and g(x) = 0.5x + 1.5 are inverse functions.
In this section we define one-to-one and inverse functions. We also discuss a process we can use to find an inverse function and verify that the function we get from this process is, in fact, an inverse function.