posted by Erica

Use the derivative to determine whether the function is strictly monotonic on its entire domain and therefore has an inverse function.

f(x) = cos [(3x)/2]

  1. MathMate

    Find f'(x) and solve for f'(x)=0.

    If f'(x) has one or more extrema, i.e. where f"(x)≠0, then the function is not monotonic, and an inverse is undefined on its entire domain.

    For the case of f(x)=cos(x), there should be an infinite number of extrema.

Respond to this Question

First Name

Your Answer

Similar Questions

  1. inverse

    If f(x)=cosx + 3 how do I find f inverse(1)?
  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. Calc

    Show that f is strictly monotonic on the given interval and therefore has an inverse function on that interval. f(x) = abs. val. (x + 2), [-2, infinity)
  4. Calc. checking answer

    Determine whether or not each of the following functions is invertible. Give your reasons for believing the function is invertible or not. Please check this for me. I am not sure if I am adequately explaining my answer and if my answer …
  5. 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. …
  6. Calculus, check my answers, please! 3

    Did I get these practice questions right?
  7. calculus

    1. Which of the following expressions is the definition of the derivative of f(x) = cos(x) at the point (2, cos(2))?
  8. calculus

    8. Find the derivative of the function f(x) = cos^2(x) + tan^2(x) 9. Find f '(x) for f(x) = xln(x) - 5ex. 10. Find f '(x) for f (x) = e(^lnx) + e^(x)ln(x) 11. Find the x-coordinate where the graph of the function f(x) = e^(-cosx) has …
  9. Calc AB

    Remember that f(x) must be one-to-one (only one y-value for each x-value) over the domain where f –1(x)is defined as a function. So, in some cases you must restrict the domain of f(x) so that it's one-to-one. There might be more …
  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