precalc

posted by .

How would you find the inverse of these two functions: f(x)=4/(x-4)^2 and
f(x)=x^2-8x+16

could you please show me step by step i have been trying to figure it out for hours.

  • precalc -

    first one:
    y = 4/(x-4)^2
    inverse is
    x = 4/(y-4)^2
    solving this for y .....
    (y-4)^2 = 4/x
    y - 4 = ± 2/√x
    y = 4 ± 2/√x

    2nd .....
    inverse is
    x = y^2 - 8y + 16
    y^2 - 8y + 16 - x = 0
    use the quadratic equation
    where a=1, b=-8 and c = 16-x to solve for y

  • precalc -

    thanks i got the first one now!

    for the second one I used the quadratic eqn and got 4 but that is not the answer?

  • precalc -

    y = (8 ± √(64-4(1)(16-x))/2
    = (8 ± √(4x) )/2
    = (8 ± 2√x)/2
    = 4 ± √x

    check: let x = 3 into the first
    y = 9 - 24 + 16 = 1

    put x = 1 into the second:
    y = 4 ± √1 = 5 or 3

    notice the the inverse of each of the equations is not a function.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    Could you show me step by step how to find the inverse of this problem: log with base of 2 (x+1) Thanks! It is not clear what the problem is. You are given a function of x. Let's calli it y. Are you trying to come up with an equation …
  2. Physics

    I'm trying to rearange this 0 = Xo + 2^-1 a t^2 for t I've been told that it is (a^-1 2x)^(2^-1) but I do not see how please show me step by step how you get that 0 - Xo = Xo - Xo + 2^-1 a t^2 (-Xo = 2^-1 a t^2) a^-1 2 (a^-1 (2-Xo) …
  3. precalc(help!!)

    I have been trying to figure this out for hours and I still cant figure it out! Please help me.. The question says to find the value of theta when sin(theta)=0 the answers include equations like pi/2 +2piK 0=2piK pi/2+pik pik
  4. functions

    For each problem, construct two composite functions, . Evaluate each composite function for x=2 ok i have not dealt with composite functions can I please get some help with this as I have 20 questions to do can someone show me step …
  5. two step equation-fraction

    I need step by step how to get the answer, I have been trying for hours, 4+m divided by 3 = 5/6 i have the answer just don't know the steps to get to the answer. m= -3/2 or 1 1/2
  6. math

    An equation and the steps to solve it are shown below: 3x − one over two (8x − 2) = 4 Step 1: 3x − 4x + 1 = 4 Step 2: x + 1 = 4 Step 3: x + 1 − 1 = 4 − 1 Step 4: x = 3 Which step was the error made and …
  7. math

    An equation and the steps to solve it are shown below: 3x − one over two (8x − 2) = 4 Step 1: 3x − 4x + 1 = 4 Step 2: x + 1 = 4 Step 3: x + 1 − 1 = 4 − 1 Step 4: x = 3 Which step was the error made and …
  8. Math

    Find the exact roots of 0= x^2 -7x +7 I think you have to use the quadratic formula, but I can't figure out how to do this or how to verify. If you could show me step by step, that would be awesome. Thanks
  9. Pre-calc

    HI, can someone can please help me find the coordinates of the two halfway points of the principal cycles. Here are some answers that might help. -I found the interval: (0,pi/2) -The equation of the left vertical asymptote: x=0, and …
  10. PreCalc

    Approximate the solutions to the following equation on the interval [0,2π). Round your answer to four decimal places. sinθ=0.65 Apparently, there suppose to be two answers to this question with a comma separating​ both …

More Similar Questions