First slide

Functions (XII)

Question

If f is periodic, g is polynomial function and $f (g (x))$ is periodic and g(2) = 3, g(4) = 7 then g(6) is ______

Moderate

A

11
B

22
C

10
D

24

Solution

From the given date g(x) must be linear function. Hence, g(x) = ax + b
Also $g (2) = 2 a + b = 3 and g (4) = 4 a + b = 7$
solving, a = 2 and b = -1
Hence, $g (x) = 2 x - 1$ Then, $g (6) = 11$

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