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3. Use the following functions of x E R' to answer the rest of this question: 1 f(x) 1 =; 9(x) = ; h(x) = 3x; w(x) = In(x) %3D (a) Which of the following are continuous? Also state the domain of each, and whether the relevant function is one-to-one. i. h (x) + w (x) ii. f (x) o g (x)

3. Use the following functions of x E R' to answer the rest of this question: 1 f(x) 1 =; 9(x) = ; h(x) = 3x; w(x) = In(x) %3D (a) Which of the following are continuous? Also state the domain of each, and whether the relevant function is one-to-one. i. h (x) + w (x) ii. f (x) o g (x)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Hello,

I am writing Mathematical Methods for Economists soon.

And I'm struggling with the questions attached.

 

Is there a easy/quick way to check if a function is:

continuous, one-to-one, onto, the domain and range?

 

Example, what should I look for in each equation to answer the questions?

 

3. Use the following functions of x E R' to answer the rest of this question: 1 f (x) 1 = ; g(x) = z; h(x) = 3x; w(x) = In(x) (a) Which of the following are continuous? Also state the domain of each, and whether the relevant function is one-to-one. i. h (т) + w (х) ii. f (x) o g (x) 4. For each of the following functions, state the domain, the range, whether it is onto and whether it is one-to-one. If a function is one-to-one, give the inverse. (a) f(x) = 7x + 3 (b) g(x) = x³,where x > 0 (c) f(x) = 1 1+x²
Transcribed Image Text:3. Use the following functions of x E R' to answer the rest of this question: 1 f (x) 1 = ; g(x) = z; h(x) = 3x; w(x) = In(x) (a) Which of the following are continuous? Also state the domain of each, and whether the relevant function is one-to-one. i. h (т) + w (х) ii. f (x) o g (x) 4. For each of the following functions, state the domain, the range, whether it is onto and whether it is one-to-one. If a function is one-to-one, give the inverse. (a) f(x) = 7x + 3 (b) g(x) = x³,where x > 0 (c) f(x) = 1 1+x²
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