The function fx 7 dx5x is onetoone Find the inverse of f S

The function f(x) = 7 - dx/5x is one-to-one. Find the inverse of f. State the domain and range of f. State the domain and range of f^-1. What is the inverse of f/What is the domain and range of f? What is the domain and range of f^-1

Solution

f(x) = ( 7-6x)/5x

y =  ( 7-6x)/5x

To find inverse plug x= y and y = x and solev for y:

y = ( 7-6x)/5x

x= ( 7- 6y)/(5y)

5xy = 7 -6y

y( 5x +6) =7

y = 7/(5x +6)

a) f^-1(x) = 7/(5x +6)

b) f(x) = (7 -6x)/5x

Domain: all real except x=0

So, ( -inf , 0) U (0, inf)

Range : ( -inf , -6/5) U ( -6/5 , inf)

c) Domain : denominator is zero at 5x+6 =0

x= -6/5

Domain : ( -inf, -6/5) U ( -6/5 , inf)

Range : ( -inf, 0) U ( 0, inf)