Show that f(x)=2x+3 and g(x)=x-3/2 are inverses

Question

Please show work

Show that f(x)=2x+3 and g(x)=x-3/2 are inverses

Answer 1

To show that f(x) and g(x) are inverses lets look at at f(x) and rewrite it so f(x) is replaced with y:

y = 2x+3

Now rewrite the equation, but switch the location of y and x:

x = 2y+3

Now solve the equation for y:

1. subtract 3 to each side of the equation
2. x-3 = 2y
3. divide both sides of the equation by 2
4. (x-3)/2 = y

Now replace the y with g(x)

g(x) = (x-3)/2 —> this matches the g(x) given in the problem so f(x) and g(x) are inverses.