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

Answer:

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

Step-by-step 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)