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6. Functions f and g are defined by Solve the equation f(x) = g(2) f:x-10-31, 10 xeR XER. **

6. Functions f and g are defined by Solve the equation f(x) = g(2) f:x-10-31, 10 xeR XER. **

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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6. Functions f and g are defined by 10-31, 10 3-2x Solve the equation If(x) = g(2). 7. The functions f and g are defined for x > 0 by f:x+21² +3. g:x+3x+2. (1) Show that gf(x) = 61² +11 and obtain an unsimplified expression for fg(x). (ii) Find an expression for (fg)"¹(x) and determine the domain of (fg)¹. (iii) Solve the equation gf(2x) = (g(x). 8.* (1) Express 4x² + 12x + 10 in the form (ax + b)2+c, where a, b and care constants. (II) Functions fand g are both defined for x>0. It is given that f(x)=x²+1 and fg(x)=4x² + 12x + 10. Find g(x). (iii) Find (fg)'(x) and give the domain of (fg)"¹, 9.* The functions f and g are defined by f(x) x)=4-2 forx>0. g(x) = 5x+2 for x > 0. (1) Find and simplify an expression for fg(x) and state the range of fg. (ii) Find an expression for g(x) and find the domain of g 10.* The function f is defined by f(x) = 3x + 1 for x a., where a is a constant. The function g is defined by g(x)=-1-² for x < -1. (i) Find the largest value of a for which the composite function gf can be formed. For the case where a = -1. (ii) solve the equation fg(x) + 14 = 0, (iii) find the set of values of x which satisfy the inequality gf(x) < -50. To be handed in by Wednesday 15th June, 2022. Please include your name & group name on any work handed in. f:x g: x xeR. XER. X*
Transcribed Image Text:6. Functions f and g are defined by 10-31, 10 3-2x Solve the equation If(x) = g(2). 7. The functions f and g are defined for x > 0 by f:x+21² +3. g:x+3x+2. (1) Show that gf(x) = 61² +11 and obtain an unsimplified expression for fg(x). (ii) Find an expression for (fg)"¹(x) and determine the domain of (fg)¹. (iii) Solve the equation gf(2x) = (g(x). 8.* (1) Express 4x² + 12x + 10 in the form (ax + b)2+c, where a, b and care constants. (II) Functions fand g are both defined for x>0. It is given that f(x)=x²+1 and fg(x)=4x² + 12x + 10. Find g(x). (iii) Find (fg)'(x) and give the domain of (fg)"¹, 9.* The functions f and g are defined by f(x) x)=4-2 forx>0. g(x) = 5x+2 for x > 0. (1) Find and simplify an expression for fg(x) and state the range of fg. (ii) Find an expression for g(x) and find the domain of g 10.* The function f is defined by f(x) = 3x + 1 for x a., where a is a constant. The function g is defined by g(x)=-1-² for x < -1. (i) Find the largest value of a for which the composite function gf can be formed. For the case where a = -1. (ii) solve the equation fg(x) + 14 = 0, (iii) find the set of values of x which satisfy the inequality gf(x) < -50. To be handed in by Wednesday 15th June, 2022. Please include your name & group name on any work handed in. f:x g: x xeR. XER. X*
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