Given that f(x)=x, g(x)=x-1: h(x)=sqrtx-1.
find f0g0h.
As posted, h(x) is interpreted as sqrtx-1 = sqrt(x)-1. If h(x) is meant to be sqrt(x-1), you only have to make appropriate changes to get the right answer. In general, be sure to include all required parentheses in posts.
f(x)=x
g(x)=x-1
h(x)=sqrt(x)-1
Since composition of functions is associative, i.e.
f ° (g ° h) = (f ° g) ° h,
the order of composition is not important.
(f°g°h)(x)
= f°(g(h(x)))
=f(g(h(x)))
=f(g(sqrt(x)-1))
=f(sqrt(x)-1 -1)
=sqrt(x)-2
To find f0g0h, we need to evaluate the composition of the three functions: f(g(h(x))).
First, let's find h(x):
h(x) = sqrt(x - 1)
Next, let's find g(h(x)):
g(h(x)) = h(x) - 1 = sqrt(x - 1) - 1
Finally, let's find f(g(h(x))):
f(g(h(x))) = g(h(x)) = sqrt(x - 1) - 1
Therefore, f0g0h = sqrt(x - 1) - 1.