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Hence inverse of the function h is
h⁻¹ :x→ 2/(x-1) -1
An inverse function is a function that "undoes" the action of another function. In other words, if a function f(x) takes an input x and produces an output y, then its inverse function, denoted as f⁻¹(y) or sometimes as g(y), takes the output y and produces the input x such that f(x) = y.
A function is a rule that associates each element of a set (called the domain) with a unique element of another set (called the range or codomain).
Given function
f(x)=1+1/x for x>0
g(x)=(x+1)/2 for x>0
Given: h=fg
h=f(g(x))
h=1+1/(x+1)/2
Now, taking the inverse of the function h,
h=1+1/(x+1)/2
h-1=1/(x+1)/2
1/(h-1)=(x+1)/2
2/(h-1)=x+1
x=2/(h-1) -1
Hence inverse of the function h is
h⁻¹:x→ 2/(x-1) -1
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