Question 1120562
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<pre>
You want to have, as the problem requires


    |x^2 -9|  <=  0.2.


It means


    -0.2 <= x^2 - 9 <= 0.2


    9-0.2 <= x^2 <= 9+0.2


    8.8   <= x^2 <= 9.2.      Now take the square root from both sides


    {{{sqrt(8.8)}}} <= x <= {{{sqrt(9.2)}}}       (1)


Notice that  {{{sqrt(8.8)}}} = 2.966. . .   and  {{{sqrt(9.2)}}} = 3.033.


Therefore,  inequality (1)  implies


     2.966 <= x <= 3.033    (with 3 decimals after the decimal point).


It means that  |x - 3|  <= 0.033.


<U>Answer</U>.  If x is within  0.033  units of 3, then f(x) is within 0.2 units of 9.
</pre>


Notice that {{{sqrt(0.2)}}} = 0.447  (approximately.


Therefore,  it is NOT ENOUGH to have  |x-3| <= sqrt(0.2) in order for the required inequality was in place.


It shows that the solution by the other tutor is incorrect.