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...
Related questions
Question
![Consider the function
f(z) = 4x + e² +5 with g(z) = f¯1 (z).
(a) Show that f (x) is one-one on R.
(b) Find g' (6).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb2f5b0ad-df1d-48c6-a9a3-5338b8167143%2F32fa398b-fe47-4fe4-804d-88d38a9efb26%2Fn8v3y3_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Consider the function
f(z) = 4x + e² +5 with g(z) = f¯1 (z).
(a) Show that f (x) is one-one on R.
(b) Find g' (6).
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
Step 1
(a)
From the definition of one to one function, if there doesn't exist such y in its codomain such that it has more than one preimage (x) in its domain, then such function will be one to one function. It means, the function must have only one x for one y. Graphical it can be interpreted as if the function is strictly increasing or decreasing in its domain, then the function be called as one to one.
Here, if we prove the given function is strictly increasing or decreasing then we can definitely say that this function is one to one.
So, differentiate the given function with respect to x,
Here , so
Therefore, f '(x) > 0 in its domain, it means the function is strictly increasing, so this is one to one function.
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