If (f(x) = frac{4}{x} – 1, x neq 0), find (f^{-1}(7)).
-
A.
(frac{-3}{7}) -
B.
(0) -
C.
(frac{1}{2}) -
D.
(4)
Correct Answer: Option C
Explanation
(f(x) = frac{4}{x} – 1). Let y = f(x)
(y = frac{4 – x}{x} implies xy + x = 4)
(x(y + 1) = 4 therefore x = frac{4}{y + 1})
(f^{-1}(7) = frac{4}{7 + 1} = frac{1}{2})