How do you find the compositions given # f(x)=x+2# and #g(x)= sqrtx#?

1 Answer
Alan P.
Dec 19, 2015

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

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

Explanation:

It can be confusing to have #x# appear in both base equations; so it might help to convert #f(x)# to #f(a)#
#color(white)("XXX")f(x)=x+2color(white)("XXX")rarrcolor(white)("XXX")f(a)=a+2#
It then becomes easier to think of replacing #a# with #g(x)#
#color(white)("XXX")f(g(x))=g(x)+2 = sqrt(x)+2#

Similarly to evaluate #g(f(x))#

Note you may encounter the following:
#color(white)("XXX")f(g(x))# written as #fog(x)#
and
#color(white)("XXX")f(f(x))# written as #gof(x)#
Use whichever form you or your instructor prefer.

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