Consider the function fx 5 3x1 2xProve that fx is onetoon

Consider the function, f(x = 5 + 3x)/1 - 2xProve that f(x) is one-to-one. Find f^-1(x).

f(x) = ( 5 + 3x ) / ( 1-2x)

to check if a function is one to one we check that f(a) = f(b)

this means a = b

f(a) = 5 + 3a / 1-2a

f(b) = 5+3b / 1-2b

(5+3a) / (1- 2a) = (5+3b) / (1-2b)

on simplifying this equation we get

( 5 + 3a)(1-2b) = (5+3b)(1-2a)

-15b = -15 a

hence a = b

therefore, it is one to one function

2) f^-1 (x)

let y = ( 5+3x)/(1-2x)

switch x and y

x = (5+3y) / ( 1- 2y )

x - 2xy = 5+3y

-2xy - 3y = 5 - x

y = (5-x) / (-2x-3)

f^-1(x) = (x-5) / (2x+3)