Two functions f and g are defined on the set R of real numbers by (f : x to 2x – 1) and (g : x to x^{2} + 1). Find the value of (f^{-1} circ g(3)).
-
A.
12 -
B.
11 -
C.
(frac{11}{2}) -
D.
(frac{9}{2})
Correct Answer: Option C
Explanation
(f(x) = 2x – 1; g(x) = x^{2} + 1)
(f(x) = 2x – 1)
(f(y) = 2y – 1 )
(x = 2y – 1 implies 2y = x + 1)
(y = frac{x + 1}{2})
(g(3) = 3^{2} + 1 = 10)
(f^{-1}(10) = frac{10 + 1}{2} = frac{11}{2})