For the functions: f(x) =1/x^2  g(x)= 7x-6  h(x)= 1-2x, Find. a) f o g(x) b) g o f o (x)c) Given f(x) = 3x + 5   h(x)=3x^(2) + 3x + 2 Find a function g(x) so that f o g(x) = h(x)

Expert Answers
mlehuzzah eNotes educator| Certified Educator















Think of this as:

f is a rule, or sort of a procedure.

You start with x, multiply by 3, then add 5

but you don't have to start with x
you can start with a number, for example, 2

then f, our rule, does the following to 2:

start with 2, multiply by 3, then add 5
so f(2)=3(2)+5=11

or you could start with something more complicated-looking, like g(x)

but still you are just doing f to the thing "g(x)":

start with g(x), multiply by 3, then add 5
so f(g(x))=3g(x)+5

so if we want `f@g(x)=h(x)`

really we want:


subtract 5 from both sides:


divide both sides by 3:


So that is the function g(x) such that f(g(x))=h(x)