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Question
Make x the subject of the formula y = `(1 - x^2)/(1 + x^2)`. Find x, when y = `(1)/(2)`
Solution
y = `(1 - x^2)/(1 + x^2)`
⇒ y(1 + x2) = 1 - x2
⇒ y + yx2 = 1 - x2
⇒ yx2 + x2 = 1 - y
⇒ x2( 1 + y) = 1 - y
⇒ x2 = `(1 - y)/(1 + y)`
⇒ x = `sqrt((1 - y)/(1 + y)`
Substituting y = `(1)/(2)`, we get
x = `sqrt((1 - 1/2)/(1 + 1/2)`
= `sqrt(1/3)`.
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