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Cartesian Product

149. If f(x)=...

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149. If f(x)=ax+b/cx+d, then (fof)(x)=x,prove that d+a=0

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f (x) = \frac{a x + b}{c x + d}

(f o f) x = x,

f (x) = \frac{a x + b}{c x + d}

f o f (x) = x

, provided that

f (x) = \frac{a x + b}{c x + d}

. Then fof(x) = x provided that.

f (x) = \frac{a x + b}{c x + d}

(f o f) (x) = x

f (x) = f (x - a) (x - b) (x - c) (x - d)

then prove that

Δ = ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} a & x & x & x x & b & x & x x & x & c & x x & x & x & d \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ = f (x) - x f^{^{'}} (x) .

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