Question

How do you find the (f o g o h) (x) for `f(x)=(x-2)/(2x+1),`g(x)=3x+1`,`h(x)=x^2#?

Answer 1

In this problem, ƒ o g o h = ƒ(g(h(x)))

Explanation:

Start out by plugging h into g.

ƒ(g(`x^2`)))

=ƒ(3(`x^2`) + 1)

= ƒ(`3x^2` + 1)
Next, plug in the new function into ƒ.

= `(3x^2 + 1 - 2) / (2(3x^2 + 1) + 1)`

= `(3x^2 - 1) / (6x^2 + 3)`