Let f(x)=√ 5 − x + 7 . Determine f ^− 1 ( x ) and the domain of f^ − 1 ( x ) . Determine f^-1(x) and the domain of f^-1(x)

Question

Let . Determine  and the domain of .



Answer 1

f(x) = √5 - x + 7; ; domain (- ∞, 5]; range [7, ∞).

y = √5 - x + 7; x = √5 - y + 7; (x - 7)² = 5 - y; y = 5 - (x - 7)²;

f^-1(x) = 5 - (x - 7)²; domain: X ≥ 7, range: y ≤ 5.