Question

What is the inverse of f(x) 3 - (1/(x+6)^2)

Answer 1

To find the inverse, simply solve for "x" in terms of "y". Replace every "x" in f(x) with 'y' and then set it equal to 'x' and then solve for 'x'

Answer 2

ok so... x = 3 - (1/(y+6)^2)
x - 3 = - (1/(y+6)^2
\[\sqrt{x-3} = -1/(y+6)\]
And I don't know where to go from there

Answer 3

x - 3 = -1/(y+6)^2

3-x = 1/(y+6)^2

(y+6)^2 = 1/(3-x)

now take square root both sides

Answer 4

so the inverse is \[\sqrt{1/(3-x)}\]

Answer 5

taking square root gives us two values for right hand side

Answer 6

x - 3 = -1/(y+6)^2

3-x = 1/(y+6)^2

(y+6)^2 = 1/(3-x)

now take square root both sides

\((y+6) = \pm \sqrt{\frac{1}{3-x}}\)

Answer 7

subtract 6 both sides to get y

Answer 8

\( (y+6) = \pm \sqrt{\frac{1}{3-x}} \)

subtract 6

\( y = -6 \pm \sqrt{\frac{1}{3-x}} \)