Calculus

posted by .

Find a formula for the inverse of the function. f(x) = (1 + 9x) / (8 - 4x)

  • Calculus -

    let y = (1+9x)/(8-4x)
    for inverse, interchange the x and y variables

    x = (1+9y)/(8-4y)
    now solve this for y .....

    8x - 4xy = 1 + 9y
    8x - 1 = 9y + 4xy
    y(9+4x) = 8x-1

    y = (8x-1)/(9+4x)
    or
    f^-1 (x) = (8x-1)/(9+4x)

    check with some arbitrary x
    say x = -1
    f(-1) = (1-9)/(8+4) = -8/12 = -2/3
    f^-1 (-2/3)
    = (8(-2/3) - 1)/(9 + 4(-2/3))
    = (-19/3) / (19/3)
    = -1 , as expected
    "more than likely" my answer is correct.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. math

    The cost of producing q articles is given by the function C=f(q)=100+2q. (A) Find the formula for the inverse function. (B) Explain in practical terms what the inverse function tells you. I am pretty sure the answer to A is f^-1(C)=C/2-50 …
  2. calculus

    Find a formula for the inverse of the function f(x) = (4 x-1)/(2x+3)
  3. Pre-calculus

    Given the following values for f(t): t : f(t) 3 : -7 6 : 6 9 : 19 12 : 6 15 : -7 18 : 6 a) What is the period, frequency, midline, amplitude, maximum, and minimum?
  4. calculus

    f(x) = (x+2)/(x+6) What is f^(-1)(-6)? (what is f inverse of -6) I found f' which was [(x+6)-(x+2)]/(x+6)^2 I set the function equal to -6 and found x to be -30/7. Used the formula to find inverse function: 1/f'(f^(-1)(-6)) So I replaced
  5. pre calculus

    Find the inverse of the function below. Graph the function below and the inverse. Determine the domain, range and asymptotes of the function below and the inverse function. Please show all your work. f(x) = 2e^-x + 5 Just looking at …
  6. Calculus

    Given the function" f(x)=1/4x− 3, find a formula for the inverse function.
  7. Pre-Calculus

    Find the inverse function for the function f(x)=2^(x)+1/2^(x)-1 You will need to use some properties of logarithmic functions to find the inverse of this particular function.
  8. Calculus Help

    The formula C =5/9(F − 32), where F ≥ −459.67, expresses the Celsius temperature C as a function of the Fahrenheit temperature F. Find a formula for the inverse function. What is the domain of the inverse function?
  9. Algebra

    Dan works at a hardware store. The employee discount is determined by the formula d = 0.15 (c − 10 ). Use the inverse of this function to find the cost of the item for which Dan received an $18.00 discount. a. Find the inverse …
  10. Calculus

    Hello I need help with this excersise of derivative of a inverse function. The excersise says: If f(x+2)=x^3+1 and g(x)=f(arctg x), find the derivative of the inverse function of g(x) and then calculate (g^-1 (9))'[the derivative of …

More Similar Questions