Question

refer to the image please!!

Answer 1

${ \qquad\qquad\huge\underline{{\sf Answer}}}$

Here we go ~

Value of g (x) is -2, when :

$\qquad \sf  \dashrightarrow \: - 2.5 < x \leqslant - 1.5$

And since -2 lies in this range of x,

$\qquad \sf  \dashrightarrow \:g( - 2) = - 2$

Value of x is -1, when :

$\qquad \sf  \dashrightarrow \: - 1.5 < x \leqslant - 0.5$

And -0.5 falls in this range, hence

$\qquad \sf  \dashrightarrow \:g( - 0.5 ) = - 1$

Next, The value of x is 0 when :

$\qquad \sf  \dashrightarrow \: - 0.5 < x < 0.5$

But, it isnt equal to 0.5, since there is open interval at both extremes.

Next, Value of x is 1, when :

$\qquad \sf  \dashrightarrow \:0.5 \leqslant x < 1.5$

And since it also has the value 0.5 included in it,

$\qquad \sf  \dashrightarrow \:g(0.5) = 1$