Math

posted by .

Find the inverse function of f

f(x) = x^2 + x, x >(or equal to) (-1/2)

Thanks!

  • Math -

    let y = x^2 + x , x ≤ -1/2
    the inverse is
    x = y^2 + y

    solving for y ...

    y^2 + y - x = 0
    y = (-1 ± √(1 - 4x))/2

    f(x) = -1/2 ± √(1-4x)/2 where x ≤ 1/4
    but in the original we are only considering the left "wing" of the parabola, so in the inverse we have to consider only
    f(x) = -1/2 - √(1-4x)/2 , for x ≤ 1/4

    testing:
    in original, let x = -5
    f(-5) = 25-5 = 20 , point is (-5,20)

    in the inverse
    f(20) = -1/2 - √81/2 = -1/ - 9/2 = -5

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. inverse

    find f^-1 (x). (this is asking me to find the inverse) f(x) = -(x-2)^2, x <= 2 how do I solve this problem?
  2. algebra

    1 (a) A function passes through the points (0, -5), (1, 0), (2, 7). Use finite differences to determine the equation of the function. (b) Draw the graph of the function. (c) Draw the inverse on the graph. (d) Show at least two different …
  3. 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 …
  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. Math 3

    Find the inverse of the function f(x) = 5 – e^(x-1). Determine the domain, range, and asymptotes of the function and its inverse function. Please show all of your work.
  6. Calculus

    F(x) = 1-x and g(x) = 1/x These functions have the property that f = f^-1(inverse) and g = g ^-1. That is, the inverse of f is equal to itself and the inverse of g is also equal to itself. Take the composition of each function with …
  7. 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 …
  8. College Algebra

    Find the inverse of the function below. Graph the function below and the inverse function. Determine the domain, range, and asymptotes of the function below and the inverse function. Please show all of your work. Show both graphs. …
  9. Algebra

    Myra uses an inverse variation function to model the data for the ordered pairs below. (2, 30), (3, 20), (4, 15), (5, 12), (6, 10) Which statement best explains whether an inverse variation function is the best model for the data?
  10. Math

    Find inverse of f if f(x)= x^2-4x+3, (for x is smaller than and equal to 2). First prove that f(x) is one to one in the defined domain of f and then obtain the inverse function. I know how to find the inverse. We just switch x and …

More Similar Questions