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7. We define f: R R as follows: {. f(x) = X -x3 if x ≥ 1, if 0 < x < 1, if x < 0. (a) Calculate f(3), ƒ(1/3), f(-1/3), and f(-3). (b) Sketch a graph of f. (c) Find Im(f).

7. We define f: R R as follows: {. f(x) = X -x3 if x ≥ 1, if 0 < x < 1, if x < 0. (a) Calculate f(3), ƒ(1/3), f(-1/3), and f(-3). (b) Sketch a graph of f. (c) Find Im(f).

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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7. We define f: R→ R as follows: x3 -{. f(x) = X if x ≥ 1, if 0 < x < 1, if x < 0. -x3 (a) Calculate f(3), ƒ(1/3), ƒ(-1/3), and f(-3). (b) Sketch a graph of f. (c) Find Im(f).
Transcribed Image Text:7. We define f: R→ R as follows: x3 -{. f(x) = X if x ≥ 1, if 0 < x < 1, if x < 0. -x3 (a) Calculate f(3), ƒ(1/3), ƒ(-1/3), and f(-3). (b) Sketch a graph of f. (c) Find Im(f).
Expert Solution
Step 1

Given a function f:R→R defined as follows

fx=x3       if x≥1x        if 0≤x<1−x3    if x<0

a We have to calculate f3, f13, f−13 and f−3.

For x=3, function fx=x3

Hence, f3=27.

For x=13, function fx=x

Hence, f13=13.

For x=-13, function fx=-x3

Hence, f-13=-127.

For x=-3, function fx=-x3

Hence, f-3=-27.

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