Question

Find the range of the real valued function log|4-x²|

Answer 1

hey mate!

4−x2≥0⇒(2−x)⋅(2+x)≥0

which holds for

[−2,2]hence

D(f)=[−2,2]

The range is

y=√4−x2⇒y2=4−x2⇒x2=4−y2≥

0⇒(2−y)(2+y)≥0

Because y≥0

we have that R(f)=(0,2)