Question -
Answer -
Given f(x) =sin┬аx┬аand┬аg(x) = 2x
We┬аknow┬аthat
f:┬аRтЖТ┬а[тИТ1,┬а1]┬аand┬аg:┬аRтЖТ┬аR
Clearly,┬аthe┬аrange┬аof┬аf┬аis┬аa┬аsubset┬аof┬аthe┬аdomain┬аof┬аg.
gof:┬аRтЖТ┬аR
(gof)┬а(x)┬а=┬аg┬а(f┬а(x))
=┬аg┬а(sin┬аx)
=┬а2┬аsin┬аx
Clearly,┬аthe┬аrange┬аof┬аg┬аis┬аa┬аsubset┬аof┬аthe┬аdomain┬аof┬аf.
fog:┬аR┬атЖТ┬аR
So,┬а(fog)┬а(x)┬а=┬аf┬а(g┬а(x))
=┬аf┬а(2x)
=┬аsin┬а(2x)
Clearly,┬аfog тЙаgof
Hence they are notequal functions.