Question

`f: { 1, 2, 3, 4} -> {1, 4, 9, 16} and g: {1, 4. 9, 16) ->{1,1/2,1/3,1/4}` are two bijective functions such that `x_1 gt x_2 => f(x_1) lt f(x_2),g(x_1) gt g(x_2)` then `f^-1(g^-1(1/2))` is equal to
A. 1
B. 4
C. 16
D. 2

Answer 1

Correct Answer - D
Clearly, f is decreasing and g is increasing
`therefore f(1)=16, f(2)=9, f(3)=4 and f(4)=1`
`and, g(1)=(1)/(4), g(4)=(1)/(3),g(9)=(1)/(2) and g(16)=1`
`therefore f^(-1)(g^(-1)((1)/(2)))=f^(-1)(9)=2`