How do you determine #f(g(x))# and #g(g(x))#, given #f(x)=sqrt(x^2+2)# and #g(x)=x^2#?

2 Answers
Shwetank Mauria
Jun 5, 2017

#f(g(x))=sqrt(x^4+2# and #g(g(x))=x^4#

Explanation:

As #f(x)=sqrt(x^2+2)# and #g(x)=x^2#

#f(g(x))=sqrt((g(x))^2+2)=sqrt((x^2)^2+2)#

= #sqrt(x^4+2#

and #g(g(x))=(x^2)^2=x^4#

Jim G.
Jun 5, 2017

#f(g(x))=sqrt(x^4+2)#
#g(g(x)=x^4#

Explanation:

#"for " f(g(x))" substitute " x=x^2" into " f(x)#

#rArrf(g(x))=f(color(red)(x^2))=sqrt((color(red)(x^2))^2+2)=sqrt(x^4+2)#

#"for " g(g(x))" substitute " x=x^2" into " g(x)#

#rArrg(g(x))=g(color(red)(x^2))=(color(red)(x^2))^2=x^4#

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