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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