Question

If f(x) =
${(x - a)}^{2}$
${(x - b)}^{2}$
, find f(a+b).​

Answer 1

Given:

f(x) =

${(x - a)}^{2}$

${(x - b)}^{2}$

To Find:

f(a+b).

Answer:

$\dfrac{b^2}{a^2}$

f(x) = $\dfrac{(x-a)^2}{(x-b)^2}$

Hence, for f(a+b) :

f(a+b) = $\dfrac{((a+b)-a)^2}{((a+b)-b)^2}\\\\\\\implies \dfrac{(a+b-a)^2}{(a+b-b)^2}\\\\\\\implies\dfrac{(b)^2}{(a)^2}\\\\\\\implies\dfrac{b^2}{a^2}$