Question

f(x)=√(4-x²), 0 ≤ x ≤ 2
Find the inverse

Answer 1

\[f(x) = \sqrt{4-x^2} = y\]
\[4-x^2 = y^2\]
\[-x^2 =-4+ y^2\]
\[x^2 =4- y^2\]
\[ \sqrt{x^2} = \sqrt{4- y^2}\]
\[ x = \sqrt{4- y^2} = g(y)\]
g is the inverse of f on
\[0\le y\le2\]