Question 3.(a) Let f: R → R, f(x)=2³+1. Is this function onto its indicatedcodomain? Prove your answers.(b) Let f: R→ R, f(x) = |x| − 1. Is this function one-to-one? Prove youranswers.(c) Let f: (-∞, 0] → [-1,∞0), f(x)=x²-1. Is this a one-to-one corre-spondence? Prove your answers.

Q.3 (a) Let , . Is this function onto its indicated codomain?Prove the answer.(b) Let , . Is this…

Answered: Question 3. (a) Let f: R→ R, f(x) =…

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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Which of the following best describes the effect of f -1 , given f is a one-to-one function and f (d) = c ? O (A) f-l inverts the input to f, sof-' (d) = 1 d (B) ƒ-l inverts the input to f, sof- (d) 1 O (C) f-l inverts the input to f, sof - f (d)) = d %3D (D) f-l inverts the input to f, sof- (d) 1 f(d) (E) The first and third options are both correct
Let f(x) = (x – 3)2 Find a domain on which f is one-to-one and increasing. Write your answer in interval notation and use two lower case o's, oo , for infinity and -00 for negative infinity. Find the inverse of f restricted to this domain f-'(x) = 1
Consider the function f(x) that is described by the statment: " the function decreases to the point (-3, -2) and then increases to the point (2,4) and then decreases again". [A: 4] A. Sketch f(x) roughly. B. Determine the interval where the first derivative is positive or negative. C. Determine the sign (+/ -) of the value of f" (-3) and f" (2)

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Question 3. (a) Let f: R→ R, f(x) = 2³+1. Is this function onto its indicated codomain? Prove your answers. (b) Let f: R→ R, f(x) = |x|- 1. Is this function one-to-one? Prove your answers. (c) Let f: (-∞0, 0] → [-1,00), f(x)=x²-1. Is this a one-to-one corre- spondence? Prove your answers.