Question

(c) Find a formula for the inverse of the function. 4x-1 ) f(x) _[3 marks] 2x+3 (ii) f(x) = /10 - 3x [2 marks) 1+1 (111) g(x) = 1-e* [3 marks] Total: 25 marks!

Answer 1

7 f(x) = 421 2x73 a f(x)=y kle know that 42-1 y 2x+ 3 42-15 > y (ax+3) 42-1 + 4(-2X-3) = 0 ( 4-24 )-1-34 x(4-24) 1 X -34 =0 34+ x 2 3y + 1 from 0. 4-2y O, we have f(x)=y of ty)=x 3y + ) 4-2 Sxtil T f ( 2 4-20

f[f=): (x4 으 fo fee) 32f 4화 다. - ) 32t) G-2) 32+). D+3 4g foft a 1t40'4t 6년 42.-12 -62 of (a) 1ee 10 g foft (2) 다. 이 oft is easts 3xt 니 (a) 4

f(x)=y (10-30 30 12 2 3 70 ECO-22) 10 f(x) = V10 -3x we known that y = y ² = 10-30 = long to-yz from le have ftly) #f1cx)) f f cy) x= Lo-y² 3 1846) boy fof'(x) = lo-X 100-my 3 3 X² fof (x)

enints fl is fta) tox 3 iii) f(x) It ez 1-ex known that 0 f(x) = 4 We 9 ya litea i-ez = ltea >) 41-ex) 1-4 y- y ez ez = 1 ex +1) yl ex yti & - log long (4) from @ have kle &=fl19 f"(9) log 191 Y+1

7 f(x) = bg x-1 foftca)= f [ log x-1 + f 2 1 Logi (2 tie log at 1 제 나 어 at 1. 저 때 72. ban exists fof '(x) = x ft 원 f(x) = 6),