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

$\displaystyle \sqrt{1+x}\approx1+\frac{1}{2}x$

which assuming means

$\displaystyle \sqrt{1+x}-0.1<1+\frac{1}{2}x<\sqrt{1+x}+0.1$

but couldn't get the given answer of

$\displaystyle -0.69<x<1.09$