Find the inverse function f1x for the given function Use com

Find the inverse function f^-1(x) for the given function. Use composition to verify that the functions are inverse. a. f(x) = -3x + 3 b. f(x) = 2/5 x - 2

Solution

a) f(x) = -3x + 3 which means y = -3x +3

to find the inverse of function, lets interchange x and y and solve for y ,

so x = -3y+3

x-3= -3y

y = (3-x)/3 = g(x)

verifying by compostion rule we will find f (g(x))

= -3*(3-x)3 +3

= x

hence verified

b) f(x) = 2/5x - 2 interchanging x and y we get

x = 2/5 y - 2

5x =2y-10

y=(5x-10)/2 = g(x)

verifying by compostion rule we will find f (g(x))

= 2/5*((5x-10)/2) - 2

= x

hence verified