Question

Determine graphically and algebraically if the two functions are inverses

1. f(x) = 2x + 3
g(x) = 2x – 3

Answer 1

So we have found algebraically that g(x) is not the inverse of f(x).

We can see graphically from the graph attached that the two lines are parallel and so g(x) cannot be the inverse of f(x).

Explanation:

i) f(x) = y = 2x + 3

replacing x with y and y with x we get

therefore x = 2y + 3

therefore
`y = (x)/(2) - (3)/(2)`

It is given that g(x) = 2x - 3.

So we have found algebraically that g(x) is not the inverse of f(x)

ii) we can see graphically from the graph attached that the two lines are parallel and so g(x) cannot be the inverse of f(x)