if f(x)=6x+3 find f^(-1) (x)

Answer 1

Turn f(x) into y.

y = 6x + 3

Switch x and y.

x = 6y + 3

Solve for y.

x - 3 = 6y

(1/6)x - 1/2 = y

Make y into f^-1(x) and put it back into the correct form.

f^-1(x) = (1/6)x - 1/2

Answer 2

To find the inverse (f^-1(x)) of a linear function, replace x with y and y with x, then solve for y in terms of x.

You have y = 6x + 3. First step is to swap y and x:

x = 6y + 3. Next, subtract 3 from both sides:

x - 3 = 6y. Then divide by 6 on both sides:

y = (1/6)x - (1/2), and that's f^-1(x): the inverse.