Consider the functions f ( x ) = - x + 5 , g ( x ) = 2 x + 3 and h ( x ) = 1 3 x - 4 . Find ( f o g ) ( x )

Given that: f ( x ) = - x + 5 , g ( x ) = 2 x + 3 and h ( x ) = 1 3 x - 4 We have to find ( f o g ) ( 4 ) As we know, f o g means g ( x ) function is in f x function That is, f o g x = - 2 x + 3 + 5 = - 2 x + 2 Hence, the value of f o g ( x ) is - 2 x + 2 .

Consider the functions f ( x ) = - x + 5 , g ( x ) = 2 x + 3 and h ( x ) = 1 3 x - 4 . Find ( h o f ) ( x )

Given that: f ( x ) = - x + 5 , g ( x ) = 2 x + 3 and h ( x ) = 1 3 x - 4 We have to find ( h o f ) ( - 7 ) As we know, h o f means f ( x ) function is in h x function That is, h o f x = 1 3 - x + 5 - 4 = - 1 3 x - 7 3 Hence, the value of ( h o f ) ( x ) is - 1 3 x - 7 3 .

Find f - 1 ( x ) for the linear function f ( x ) = 1 2 x + 4 . Give your answers in the form f - 1 ( x ) = m x + c

Given that: the linear function f ( x ) = 1 2 x + 4 . We have to find f - 1 x in the form f - 1 ( x ) = m x + c We have, f ( x ) = 1 2 x + 4 Replace f ( x ) with y . y = 1 2 x + 4 Interchange the variables. x = 1 2 y + 4 Solve for y . 2 x = y + 8 ⇒ y = 2 x - 8 Replace the y with f - 1 x to show the final answer. Hence, f - 1 ( x ) = 2 x - 8 .

E M B I B E

Mathematics : Analysis and Approaches Standard Level Course Companion>Chapter 3 - Modelling Relationships: Linear and Quadratic Functions>Exercise 3G

Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships: Linear and Quadratic Functions, Exercise 18: Exercise 3G

Author:Natasha Awada, Paul La Rondie, Laurie Buchanan & Jill Stevens

Natasha Awada Mathematics Solutions for Exercise - Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Modelling Relationships: Linear and Quadratic Functions, Exercise 18: Exercise 3G

Attempt the practice questions on Chapter 3: Modelling Relationships: Linear and Quadratic Functions, Exercise 18: Exercise 3G with hints and solutions to strengthen your understanding. Mathematics : Analysis and Approaches Standard Level Course Companion solutions are prepared by Experienced Embibe Experts.