Question

Find the fixed point of the function f. [A fixed point of a function f is a real number c such that f(c) = c.] (Round your answer to three decimal places.)

f(x)=-cos(2x)
c= ? radinas

Answer 1

The fixed point of the function f(x) = -cos(2x) is c = 0.739 radians.

Step-by-step explanation:

To find the fixed point of the function f(x) = -cos(2x), we need to find the real number c such that f(c) = c. We can do this by setting -cos(2c) = c and solving for c.

Step 1: Set -cos(2c) = c.

Step 2: Add cos(2c) to both sides: -cos(2c) + cos(2c) = c + cos(2c).

Step 3: Simplify: 0 = c + cos(2c).

Step 4: Subtract cos(2c) from both sides: -cos(2c) = c.

Step 5: Use a graphing calculator or software to find the value of c that satisfies the equation. Rounded to three decimal places, the fixed point of the function f(x) = -cos(2x) is c = 0.739 radians.

Answer 2

The fixed point of the function f(x)=-cos(2x) is approximately c = 0.739 radians.

Step-by-step explanation:

To find the fixed point of the function f(x)=-cos(2x), we need to solve the equation f(x) = x. In this case, the equation becomes -cos(2x) = x. To solve for x, we can rearrange the equation to get cos(2x) + x = 0. The fixed point c is the value of x that satisfies this equation.

We can solve this equation by using numerical methods, such as graphing or iteration. By graphing the function y = -cos(2x) and y = x, we can visually identify the point where the two graphs intersect, which represents the fixed point. Alternatively, we can use iteration by starting with an initial guess for x and repeatedly substituting it into the equation until we converge to the fixed point.

In this case, the fixed point of the function f(x)=-cos(2x) is approximately c = 0.739 radians.