Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
1. Functions f and g are defined by f:xx-7x+6 and g:xx-1 where x = 0. Show that (f.g)(x)=x²-3x² - 4x+12 (i) Solve the equation (f.g)(x)-(g.f)(x)=7 (iii) Show that (x-2) is a factor of (f.g)(x). (x=1)(.

1. Functions f and g are defined by f:xx-7x+6 and g:xx-1 where x = 0. Show that (f.g)(x)=x²-3x² - 4x+12 (i) Solve the equation (f.g)(x)-(g.f)(x)=7 (iii) Show that (x-2) is a factor of (f.g)(x). (x=1)(.

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
See similar textbooks
icon
Related questions
Question
100%

Dear expert don't Use chat gpt 

1. Functions f and g are defined by fix-x³-7x+6 and g:xx-1 where x = 0. (i) Show that (f.g)(x)=x²-3x² - 4x+12 (i) Solve the equation (f.g)(x)-(g.f)(x)=7 (iii) Show that (x-2) is a factor of (f.g)(x). (x=1). E) 2. A function h is defined by x +3 h:x: -,x # 3. X-3 (i) Show that h(3+p)+h(3-p)=2, (p>0) (ii) Find the non-zero value of q such that h(q) q-1,q*0. Ans: (q=5) 3. A function f is defined by f(x)=x+1, x-1' x #1. If (f.f)(2)=3f¹(a). Find the value of a. (a=-5) 4. Given that a b=a² + b², solve the 7 equation (2x+1)x= 8(x=-¹) ,1) 5. A function f(x)= b - -, a>0 defined for X-a all real values of x except x = a is such that f(b) = b and f(2a) = 2a. (i) Find the values of a and b. (ii) If (f.f)(x) = x, show that x²-x-2=0
Transcribed Image Text:1. Functions f and g are defined by fix-x³-7x+6 and g:xx-1 where x = 0. (i) Show that (f.g)(x)=x²-3x² - 4x+12 (i) Solve the equation (f.g)(x)-(g.f)(x)=7 (iii) Show that (x-2) is a factor of (f.g)(x). (x=1). E) 2. A function h is defined by x +3 h:x: -,x # 3. X-3 (i) Show that h(3+p)+h(3-p)=2, (p>0) (ii) Find the non-zero value of q such that h(q) q-1,q*0. Ans: (q=5) 3. A function f is defined by f(x)=x+1, x-1' x #1. If (f.f)(2)=3f¹(a). Find the value of a. (a=-5) 4. Given that a b=a² + b², solve the 7 equation (2x+1)x= 8(x=-¹) ,1) 5. A function f(x)= b - -, a>0 defined for X-a all real values of x except x = a is such that f(b) = b and f(2a) = 2a. (i) Find the values of a and b. (ii) If (f.f)(x) = x, show that x²-x-2=0
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS