Find the inverse of f(x)=6/5x-3

Answer 1

y = 6/5x-3

is it: (6/5)*x -3

or: (6/5x) - 3

or: 6/(5x - 3)

Regardless, the procedure is the same:

Isolate the x term(s) and solve for x

try this one:

y = (6/5)*x -3

(6/5)*x = -y - 3

x = -(5/6)*(y+3)

or this one:

y = (6/5x) - 3

(6/5x) = -3 -y

5x/6 = 1/(-3 -y)

x = -6/((y+3)*5)

Answer 2

Given: f(x) = 6/5x-3

Rewritten for clarity, f(x) = (6/(5x)) - 3

or y = (6/(5x)) - 3

To find the inverse function, simply swap the x and y.

From: y = 6/(5x) - 3

To: x = 6/(5y) - 3

Now solve for the y.

x + 3 = 6/(5y)

5y = 6 / (x+3)

y = 6 / (5(x+3))

y = (6/5) / (x+3)

y is the inverse function, denoted as f^-1(x).

Solution: f^-1(x) = (6/5) / (x+3)