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If `f` is periodic, `g` is polynomial function, `f(g(x))` is periodic, `g(2)=3,a n dg(4)=7,t h e ng(6)i s` 13 (b) 15 (c) 11 (d) none of these

A

13

B

15

C

11

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
From the given data, g(x) must be linear function.
Hence, `g(x)=ax+b.`
Also, `g(2)=2a+b=3 and g(4)=4a+b=7.`
Solving, we get `a=2 and b= -1`.
Hence, `g(x)=2x-1.`
Then, `g(6)=11`.
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