I don't really understand how to solve this ) : please help !
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sqrt(x) >= x
===> (sqrt(x))^2 >= x^2 ... (f(x) = x^2 is increasing for x >= 0)
===> x >= x^2
===> x^2 - x <= 0
===> x(x - 1) <= 0
===> x - 1 <= 0 ... (since x >= 0)
===> x <= 1
Combining, this gives us the solution:
0 <= x <= 1
===> (sqrt(x))^2 >= x^2 ... (f(x) = x^2 is increasing for x >= 0)
===> x >= x^2
===> x^2 - x <= 0
===> x(x - 1) <= 0
===> x - 1 <= 0 ... (since x >= 0)
===> x <= 1
Combining, this gives us the solution:
0 <= x <= 1