IDNLearn.com is designed to help you find accurate answers with ease. Find the answers you need quickly and accurately with help from our knowledgeable and experienced experts.

given that any function of f(x)=x+a/x, where a and can be any value,will have the inverse of the form f^-1(x)=a/x-1
find the inverse of f(x)=x+4/x
please add your working


Sagot :

If f^(-1) is the inverse of f, then

f(f^(-1)(x)) = x

It looks like f(x) = (x + a)/x. This gives us

f(f^(-1)(x)) = (f^(-1)(x) + a)/f^(-1)(x) = x

Solve for f^(-1)(x) :

f^(-1)(x) + a = x f^(-1)(x)

f^(-1)(x) - x f^(-1)(x) = -a

(1 - x) f^(-1)(x) = -a

f^(-1)(x) = -a/(1 - x)

f^(-1)(x) = a/(x - 1)

If a = 4, then the inverse is f^(-1)(x) = 4/(x - 1).