Test:276 QNo:1

let f(x)+f(1/x)=f(x)*f(1/x).

if f(4)=17.find f(7).

2 Answers

solve it

f(x)f(1/x) - f(x) - f(1/x) = 0

so f(x)f(1/x) - f(x) - f(1/x) + 1 = 1

[f(x) - 1 ] [ f(1/x) - 1 ] = 1

let g(x) = f(x) - 1

so g(x) g (1/x) = 1

so g(x) = Â± xⁿ

so f(x) = 1 Â±xⁿ

f(4) = 1Â±4ⁿ = 17

so n = 2

& f(x) = 1+ x²

so f(7) = 50

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