Given the functions f x = 1 2 x + 5 and g x = 4 x - 2 5 . Find g - 1 x .

Given, g x = 4 x - 2 5 We have to find g - 1 x . To find the inverse, reverse the mapping. If g maps x onto y , then g - 1 maps y onto x . To find g - 1 we have to find a value of x that corresponds to a given value of y . Let g x = y = 4 x - 2 5 ⇒ 4 x = y + 2 5 [Make x the subject of the formula, so that y maps onto x ] ⇒ x = 5 y + 2 20 g - 1 maps y onto x , so g - 1 ( y ) = 5 y + 2 20 This is usually written in terms of x , so g - 1 ( x ) = 5 x + 2 20 . Hence, g - 1 x = 5 x + 2 20

Given the functions f x = 1 2 x + 5 and g x = 4 x - 2 5 . Find g - 1 x .

Given, g x = 4 x - 2 5 We have to find g - 1 x . To find the inverse, reverse the mapping. If g maps x onto y , then g - 1 maps y onto x . To find g - 1 we have to find a value of x that corresponds to a given value of y . Let g x = y = 4 x - 2 5 ⇒ 4 x = y + 2 5 [Make x the subject of the formula, so that y maps onto x ] ⇒ x = 5 y + 2 20 g - 1 maps y onto x , so g - 1 ( y ) = 5 y + 2 20 This is usually written in terms of x , so g - 1 ( x ) = 5 x + 2 20 . Hence, g - 1 x = 5 x + 2 20

Given the functions f x = 1 2 x + 5 and g x = 4 x - 2 5 . Find the value of gf - 1 - 2 .

Given, f x = 1 2 x + 5 , g x = 4 x - 2 5 We have to find the value of gf - 1 - 2 . To find the inverse, reverse the mapping. If f maps x onto y , then f - 1 maps y onto x . To find f - 1 we have to find a value of x that corresponds to a given value of y . Let f x = y = 1 2 x + 5 ⇒ 1 2 x = y - 5 [Make x the subject of the formula, so that y maps onto x ] ⇒ x = 2 y - 5 f - 1 maps y onto x , so f - 1 ( y ) = 2 y - 5 This is usually written in terms of x , so f - 1 ( x ) = 2 x - 5 . Now, f - 1 ( - 2 ) = 2 - 2 - 5 = - 14 And, gf - 1 ( - 2 ) = g f - 1 ( - 2 ) = g - 14 = 4 - 14 - 2 5 = - 56 - 2 5 = - 56 2 5 Hence, the value of gf - 1 - 2 = - 56 2 5 .

Given the functions f x = 1 2 x + 5 and g x = 4 x - 2 5 . Find the value of f - 1 g - 1 4 .

Given, f x = 1 2 x + 5 , g x = 4 x - 2 5 We have to find the value of f - 1 g - 1 4 . To find the inverse, reverse the mapping. If f maps x onto y , then f - 1 maps y onto x . To find f - 1 we have to find a value of x that corresponds to a given value of y . Let f x = y = 1 2 x + 5 ⇒ 1 2 x = y - 5 [Make x the subject of the formula, so that y maps onto x ] ⇒ x = 2 y - 5 f - 1 maps y onto x , so f - 1 ( y ) = 2 y - 5 This is usually written in terms of x , so f - 1 ( x ) = 2 x - 5 . Let g x = y = 4 x - 2 5 ⇒ 4 x = y + 2 5 [Make x the subject of the formula, so that y maps onto x ] ⇒ x = 5 y + 2 20 g - 1 maps y onto x , so g - 1 ( y ) = 5 y + 2 20 This is usually written in terms of x , so g - 1 ( x ) = 5 x + 2 20 . And, g - 1 4 = 5 4 + 2 20 = 22 20 = 11 10 Now, f - 1 g - 1 4 = f - 1 g - 1 4 = f - 1 11 10 = 2 11 10 - 5 = 2 - 39 10 = - 39 5 = - 7 4 5 Hence, the value of f - 1 g - 1 4 = - 7 4 5 .

If S = a 1 - r , find a when S = 5 . 2 and r = 0 . 3 .

Given, S = a 1 - r Multiply each side by 1 - r , we get a = S ( 1 - r ) Substituting the values S = 5 . 2 and r = 0 . 3 , a = 5 . 2 ( 1 - 0 . 3 ) ⇒ a = 3 . 64

E M B I B E

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 22 - More Equations, Formulae and Functions>Exercise 22.8>Q 6

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Earn 100

Given the functions $f (x) = \frac{1}{2} x + 5$ and $g (x) = 4 x - \frac{2}{5}$ . Find $g^{- 1} (x)$ .

Important Questions on More Equations, Formulae and Functions

MEDIUM

Upper Secondary: IGCSE

IMPORTANT

Cambridge IGCSE® Mathematics Core and Extended Coursebook Second Edition>Chapter 22 - More Equations, Formulae and Functions>Exercise 22.8>Q 6

Given the functions $f (x) = \frac{1}{2} x + 5$ and $g (x) = 4 x - \frac{2}{5}$ . Solve $f (x) = g (x)$ giving your answer correct to two decimal places.