If fx-x-a2x-b2- find fa-b-

Given: f (x) = (x ndash; a)2(x ndash; b)2 Thus, f (a + b) = (a + b ndash; a)2(a + b ndash; b)2 nbsp; nbsp; nbsp; nbsp; nbsp; nbsp; n ...

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How to Find the Inverse of a Function

If fx=x-a2x-b...

Question

If f(x) = (x − a)² (x − b)², find f(a + b).

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Solution

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f (a + b - x) = f (x)

\int_{a}^{b} x f (x) d x = (\frac{a + b}{2}) \int_{a}^{b} f (x) d x

\int_{a}^{b}

\frac{a + b}{2} \int_{a}^{b} f (b - x) d x

\frac{a + b}{2} \int_{a}^{b} f (b + x) d x

\frac{b - a}{2} \int_{a}^{b} f (x) d x

\frac{a + b}{2} \int_{a}^{b} f (x) d x

f (a) = a^{2}, ϕ^{'} (a) = b^{2}

3 ϕ^{'} (a)

lim x \to 0 \frac{\sqrt{f (x)} - a}{\sqrt{ϕ (x)} - b}

f (a) = a^{2}, ϕ (a) = b^{2}

f^{'} (a) = 3 ϕ^{'} (a)

lim x \to 0 \frac{\sqrt{f (x)} - a}{\sqrt{ϕ (x)} - b}

f (a + b - x) = f (x)

\int_{a}^{b} x f (x) d x

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