Writing formulas f o g o h

Question

Write a formula for fg​h, where ​f(x)​=sqx+3, ​g(x) ​=1/x+4, and ​h(x)=1/x .

​(f◦g◦​h)(x)=

Answer 1

​(f◦g◦​h)(x)=f(g(h(x)))

We want to start from the inside and go out:

To find g(h(x)) we have to plug h(x) into g(x). So everywhere there is an x in g(x) we will in h(x):

g(h(x)) = 1/h(x) + 4 = 1/(1/x) + 4 = x+4

Now f(g(h(x))) = f(x+4) = sq(x+4) + 3, by plugging x+4 into the function f.