Determine whether two functions are inverses of each other

Question

a) 

f(x) = 2x+3

g(x) = x-3/2

 

f(g(x))= ?

g(f(x))= ?

 

f and g are inverses of each other OR 

f and g are not inverses of each other

b)

f(x)= -6x

g(x)= -6x

 

f(g(x))= ?

g(f(x))=?

 

f and g are inverses of each other OR

f and g are not inverses of each other

 

Answer 1

f(x) = 2x + 3

g(x) = x -3/2

f(g(x)) = 2(x-3/2) + 3 = 2x-3+3 = 2x

g(f(x)) = (2x+3)-3/2 = 2x+3/2

they are not inverses

y=2x+3

x=2y+3

2y =x-3

y = x/2 -3/2 = f^-1(x) = the inverse of f(x) but g(x) is x-3/2 not x/2-3/2

for g(x) switch x and y to get x=y-3/2, y=x+3/2 = g^-1(x)

b)

f(x) =-6x

g(x) =-6x

f(g(x)) = f(-6x) = -6(-6x) = 36x

g(f(x)) = g(-6x) = -6(-6x) = 36x

y=-6x

x=-6y

y = -x/6 = f^-1(x) = g^-1(x)

f^-1(f(x)) = f^-1(-6x) = -(-6x)/6 = x