How many solutions does the equation x=4cos(x) have if x is greater than/equal to -5 but less than/equal to 5?

Answer 1

You can't solve the equation exactly, so the easiest thing to do is just draw a graph - draw y = 4 cos x and y = x on the same axes. Then you'll easily see there are 3 answers.

Answer 2

4cos(x) = x, -5 ≤ x ≤ 5

This has 3 solutions (using Excel and x = -5 to 5)
A1 = - 5: B1 = A1 + 0.5 (Fill right to V1 giving full domain)
A2 = 4*cos(A1) - A1 (Fill right to V2 giving full range)

And then graph

The solutions are approximately -3.6, -2.2 and 1.75 (estimated from Excel graph)

Answer 3

graph it out and count the intersection points