Express the function f(x) = 1/x+1 in the form goh. If h(x) = x+1, find the function g(x).
huh? really?
g(x) = 1/x
so, f(x) = g◦h = 1/h = 1/(x+1)
To express the function f(x) = 1/(x+1) in the form goh, we need to substitute h(x) = x+1 into f(x). Let's start by substituting x+1 into f(x):
f(h(x)) = 1/[(x+1) + 1]
Simplifying,
f(h(x)) = 1/(x+2)
Now, to find the function g(x), we can rewrite f(h(x)) as g(x):
g(x) = 1/(x+2)
Therefore, the function g(x) is g(x) = 1/(x+2).
To express the function f(x) = 1/x + 1 in the form goh, we need to substitute h(x) = x + 1 into f(x).
First, let's substitute x with the function h(x) in f(x):
f(h(x)) = 1/h(x) + 1
Now, let's substitute h(x) with x + 1 in f(h(x)):
f(h(x)) = 1/(x + 1) + 1
This equation represents f(x) in the form goh, where g(x) = 1/(x + 1) + 1.