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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 :

LammettHash

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).

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