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Exercise 8.7.9. In each case, use Definition 8.7.7 to determine whether g is an inverse of f. (a) f: R →R is defined by f(x) = 9x – 6 and g: R → R is defined by g(y) = (y+ 6)/9. (b) f: R+ → R+ is defined by f(x) = 2r² and g: R+ → R+ is defined by g(y) = V/2. (c) f: R+ → R+ is defined by f(x) = 2/a and g: R+ → R+ is defined by g(y) = 2/y. (d) f: R+ → R+ is defined by f(r) = væ+1–1 and g: R+ → R+ is defined by g(y) = y² + 2y.

Exercise 8.7.9. In each case, use Definition 8.7.7 to determine whether g is an inverse of f. (a) f: R →R is defined by f(x) = 9x – 6 and g: R → R is defined by g(y) = (y+ 6)/9. (b) f: R+ → R+ is defined by f(x) = 2r² and g: R+ → R+ is defined by g(y) = V/2. (c) f: R+ → R+ is defined by f(x) = 2/a and g: R+ → R+ is defined by g(y) = 2/y. (d) f: R+ → R+ is defined by f(r) = væ+1–1 and g: R+ → R+ is defined by g(y) = y² + 2y.

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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Please do part a and please show step by step and explain. 

Exercise 8.7.9. In each case, use Definition 8.7.7 to determine whether g is an inverse of f. (a) f: R → R is defined by f(x) = 9x – 6 and g: R → R is defined by g(y) = (y + 6)/9. (b) f: R+ → R+ is defined by f(x) = 2x2 and g: R+ → R+ is defined by g(y) = V/2. (c) f: R+ → R+ is defined by f(x) = 2/x and g: R+ → R+ is defined by g(y) = 2/y. (d) f: R+ → R+ is defined by f(r) = vr+1-1 and g: R+ → R+ is defined by g(y) = y² + 2y.
Transcribed Image Text:Exercise 8.7.9. In each case, use Definition 8.7.7 to determine whether g is an inverse of f. (a) f: R → R is defined by f(x) = 9x – 6 and g: R → R is defined by g(y) = (y + 6)/9. (b) f: R+ → R+ is defined by f(x) = 2x2 and g: R+ → R+ is defined by g(y) = V/2. (c) f: R+ → R+ is defined by f(x) = 2/x and g: R+ → R+ is defined by g(y) = 2/y. (d) f: R+ → R+ is defined by f(r) = vr+1-1 and g: R+ → R+ is defined by g(y) = y² + 2y.
Definition 8.7.7. Suppose f: X →Y and g: Y → X are functions. We say that g is an inverse function for the function f if and only if: 8.7 INVERSE FUNCTIONS 251 (a) f(g(y)) = y (in other words, fo g(y) = y) for all y E Y, and (b) g(f(x)) = x (in other words, gof(x) = x) for all a € X.
Transcribed Image Text:Definition 8.7.7. Suppose f: X →Y and g: Y → X are functions. We say that g is an inverse function for the function f if and only if: 8.7 INVERSE FUNCTIONS 251 (a) f(g(y)) = y (in other words, fo g(y) = y) for all y E Y, and (b) g(f(x)) = x (in other words, gof(x) = x) for all a € X.
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