verify the given linear approximation at a=0, then determine the values of x for which the linear approximation is accurate to within 0.1
which assuming means
but couldn't get the given answer of
First, we notice that the domain is .
Since both sides of the inequality are always non-negative over the domain :
Solving this gives which matches the solution you gave.
By the way, the other side doesn't actually give any restriction:
Which is always true, so there is no additional restriction here.