Find the inverse of f(x)=(3x)/(x-2)

So here are the steps to finding an inverse of a function:

Change f(x) to ySwitch the positions of x and ySolve for yChange y to f^1(x)

Firstly, apply the first two steps:

Now, let's solve for y. Firstly, multiply both sides by y-2:

Next, subtract xy on both sides:

Next, factor out y on the right side of the equation:

Lastly, divide both sides by 3 - x:

Now, apply the last step and your final answer will be

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12