Let R be the set of real numbers and f : R → R be the function defined by f (x) = 4x + 5.Show that f is invertible and find f −1

Question

Let R be the set of real numbers and f : R → R be the function defined by f (x) = 4x + 5.Show that f is invertible and find f −1
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Solution 1

To show that a function is invertible, we need to show that it is both injective (one-to-one) and surjective (onto).

  1. Injective: A function f: X → Y is said to be injective if for every x1, x2 in X, if f(x1) = f(x2), then x1 = x2. For our function f(x) = 4x + 5, let's assume f(x1) = f(x2). This g Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study prob
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
Knowee AI StudyGPT is a powerful AI-powered study tool designed to help you to solve study problem.
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