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Let f: RvecR be a continuous and differe...

Let `f: RvecR` be a continuous and differentiable function such that `(f(x^2+1))^(sqrt(x))=5forAAx in (0,oo),` then the value of `(f((16+y^2)/(y^2)))^(4/(sqrt(y)))fore a c hy in (0,oo)` is equal to (a) 5 (b) 25 (c) 125 (d) 625

A

5

B

25

C

125

D

625

Text Solution

Verified by Experts

The correct Answer is:
B
`(f((16+y^(2))/(y^(2))))^((4)/(sqrt(y)))=(f((16)/(y^(2))+1))^((4)/(sqrt(y)))`
`=(f(((4)/(y^(2)))^(2)+1))^((4)/(sqrt(y)))`
`=[(f(((4)/(y^(2)))^(2)+1))^((2)/(sqrt(y)))]^(2)`
`=5^(2)`
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