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Determine whether f(x) = 1/2 is one-to-one and find its inverse. 1. No inverse function exists. 2. f-¹(x)=x² 3. f¹(x) = x¹/2 4. None of these 5. f¹(x) = x² 1 6. f¹(x) =

Determine whether f(x) = 1/2 is one-to-one and find its inverse. 1. No inverse function exists. 2. f-¹(x)=x² 3. f¹(x) = x¹/2 4. None of these 5. f¹(x) = x² 1 6. f¹(x) =

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Determine whether f(x) == 1/2 is one-to-one and find its inverse. 1. No inverse function exists. 2. f-¹(x)=x² 3. f¹(x) = x¹/2 4. None of these 5. f¹(x) = x² 6. f¹(x) x²
Transcribed Image Text:Determine whether f(x) == 1/2 is one-to-one and find its inverse. 1. No inverse function exists. 2. f-¹(x)=x² 3. f¹(x) = x¹/2 4. None of these 5. f¹(x) = x² 6. f¹(x) x²
Expert Solution
Step 1

Solution

Given f(x)=1/x2

Let f(x)=y 

So y = 1/x2

Now replace x with y and y with x, we have 

X=1/y2

y2=1/x

So we have 2 values of y that is 

y = +1/sqrt (x)

y=-1/sqrt(x)

 

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