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2 votes
At what values of x does cos x = 7x?

a) No real solutions
b) x = 0
c) x = 1
d) Multiple solutions

1 Answer

5 votes

Final answer:

The cosine function has a range of -1 to 1, so the equation cos x = 7x can't have a solution since 7x will always be outside of this range for any real x except for 0, and at x=0 the equation doesn't hold. The correct answer is option A

Step-by-step explanation:

The question asks at what values of x does the equation cos x = 7x hold true. We know from trigonometric properties that the range of the cosine function is between -1 and 1, inclusive. Therefore, any value of x where 7x falls outside of this range would not satisfy the equality. Specifically, when x=0, we know that cos(0) = 1. Now, evaluating 7x at x=0, we also get 0. Since 1 equals 0 is a false statement, x = 0 cannot be a solution. For any other real value of x, 7x will not be between -1 and 1, making it impossible for the equation cos x = 7x to be true for any other real values of x.

To determine the values of x that satisfy the equation cos x = 7x, we need to find the intersection points of the graphs of y = cos x and y = 7x. Let's solve this equation step by step:

Plot the graphs of y = cos x and y = 7x. You can use a graphing calculator or software to visualize the two functions.

Observe the points of intersection between the two graphs. These points represent the values of x that satisfy the equation cos x = 7x.

Analyze the graph carefully to identify the solutions. From the graph, it is apparent that there are multiple solutions to the equation.

User Nevin
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