Help please?

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1 Answer
Feb 17, 2018

See below.

Explanation:

#f(x)=5/xcolor(white)(888888)# #g(x)=sqrt(36-x^2)#

#(fog)# also expressed #f(g(x))#

To find #f(g(x))#, we replace #x# in #f(x)# with #g(x)#

Then:

#f(g(x))=5/(g(x))=5/sqrt(36-x^2)#

To find the domain we recognise that, for real numbers:

#36-x^2>0#

#-x^2> -36#

#x^2<36#

Taking square root:

#x<6#

#x> -6#

#-6 < x < 6#

So the domain is:

#(-6 , 6 )#

or in set notation:

#{x in RR | -6 < x < 6}#