9. (a) Show that if a > 0 and a + 1, the function f(x) = a® is a 1-1 function. (b) For a > 0 and a + 1, define f(x) = loga x to be the inverse of a". Show that log, x is a continuous function.

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter3: Functions
Section3.3: Rates Of Change And Behavior Of Graphs
Problem 2SE: If a functionfis increasing on (a,b) and decreasing on (b,c) , then what can be said about the local...
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Answer the following showing your proofs

 

9. (a) Show that if a > 0 and a + 1, the function f(x) = a" is a 1-1 function.
(b) For a > 0 and a + 1, define f(x) = log, x to be the inverse of a".
Show that log, x is a continuous function.
Transcribed Image Text:9. (a) Show that if a > 0 and a + 1, the function f(x) = a" is a 1-1 function. (b) For a > 0 and a + 1, define f(x) = log, x to be the inverse of a". Show that log, x is a continuous function.
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