Let g : R → R be a positive function such that g(0) = 1 and g(x+y) = g(x)g(y), ∀x, y ∈ R. Show that if g is continuous at x = 0, then g is continuous at every point of R
Let g : R → R be a positive function such that g(0) = 1 and g(x+y) = g(x)g(y), ∀x, y ∈ R. Show that if g is continuous at x = 0, then g is continuous at every point of R
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter9: Systems Of Equations And Inequalities
Section: Chapter Questions
Problem 12T
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The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
Let g : R → R be a positive function such that g(0) = 1 and g(x+y) = g(x)g(y),
∀x, y ∈ R. Show that if g is continuous at x = 0, then g is continuous at every point of R
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