Question

If f(x)=2x-3/5 which of the following is the inverse of f (x)

Answer 1

For this case we must find the inverse of the following function:

`f (x) = 2x- \frac {3} {5}`

We change f(x) by y:

`y = 2x- \frac {3} {5}`

We exchange the variables:

`x = 2y- \frac {3} {5}`

We cleared "y":

Adding
`\frac {3} {5}` to both sides of the equation:

`x + \frac {3} {5} = 2y`

DIviding between 2 to both sides of the equation:

`y = \frac {x} {2} + \frac {3} {10}`

We change y for
`f^(-1) (x)`:

`f ^ {- 1} (x) = \frac {x} {2} + \frac {3} {10}`

Answer:

`f ^( - 1) (x) = \frac {x} {2} + \frac {3} {10}`

Answer 2

g(x)=(x+3/5)/2

Explanation:

When f(g(x)) and (g(f(x)) both equal x, they are inverses.

f(x)=2x-3/5

y=2x-3/5

x=2y-3/5

x+3/5=2y

(x+3/5)/2=y

(x+3/5)/2=g(x)