Part a, b, c, d, e PROBLEM 2The domain and target set of functions f and g is R. The functions are definedas:S(z) = 2x +3g(z) = 5x + 7(a) ƒog?(b) go f?(c) (S og)¯?(d) s-l og¬l?(c) g-1 of-!?Are any of the above equal?

Name: Part a, b, c, d, e PROBLEM 2The domain and target set of functions f a
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Description: Part a, b, c, d, e PROBLEM 2The domain and target set of functions f and g is R. The functions are definedas:S(z) = 2x +3g(z) = 5x + 7(a) ƒog?(b) go f?(c) (S og)¯?(d) s-l og¬l?(c) g-1 of-!?Are any of the above equal?

Answered: • S(z) = 2z + 3 • g(z) = 5z + 7 (a)…

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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Part a, b, c, d, e

PROBLEM 2
The domain and target set of functions f and g is R. The functions are defined
as:
S(z) = 2x +3
g(z) = 5x + 7
(a) ƒog?
(b) go f?
(c) (S og)¯?
(d) s-l og¬l?
(c) g-1 of-!?
Are any of the above equal?

Expert Solution

Step 1

a) fog(x) = f(g(x))

=f(5x+7)

=2(5x+7)+3

=10x+17

therefore,

fog(x)=10x+17

b) gof(x) = g(f(x))

=g(2x+3)

=5(2x+3)+7

=10x+22

therefore gof(x)=10x+22

Step 2

c) since fog(x)=10x+17

let y=10x+17

y-17=10x

x=(y-17)/10

therefore

(fog)^-1= (x-17)/10

d) f^-1(x) = (x-3)/2

g^-1(x)= (x-7)/5

so f^-1og^-1(x)= f^-1(g^-1(x))

=f^-1((x-7)/5)

= ((x-7)/5 -3)/2

=(x-22)/10

therefore f^-1og^-1 = (x-22)/10

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