Algebra math

100 points + brainy

see work below

Step-by-step explanation:

F(x)  is the same thing as y

y = 2x-3

exchange x and y

x = 2y-3

solve for y  this is how we find the inverse function

add 3 to each side

x+3 = 2y-3+3

x+3 = 2y

divid by 2

(x+3)/2 = 2y/2

(x+3)/2 = y

the inverse of F(x) is (x+3)/2

to show one function is the inverse of the other,plug that function into the inverse function.  You should get x as the answer

We will plug F(x) into G(x)

G(x) =  (x+3)/2

put (2x-3) in for x

G(x) =  ((2x-3)+3)/2

simplify the numberator

  (2x-3+3)/2

2x/2

simplify

x

Since we got x back out

F(x) and G(x) are inverses

Step 1 : y = 2x-3

Step 2 : x = 2y-3

Solve for y  

x = 2 y - 3

(+3 to both sides)

x + 3 = 2 y

(÷2 from both sides)

The inverse of F(x) is (x+3)/2

Substitute F(x) into G(x)

G(x) =  

G(x) =

(2x-3+3)/2 - Simplify

2x/2

Since the x is the same

F(x) and G(x) are inverses

Step-by-step explanation: