Home » Further Mathematics » If (f(x) = frac{4}{x} – 1, x neq 0), find (f^{-1}(7)).

If (f(x) = frac{4}{x} – 1, x neq 0), find (f^{-1}(7)).

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})