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Question

lf f(x)=g(x) and g(x)=f(x) for all x and f(2)=4=g(2), then f2(24)+g2(24) is
  1. 24
  2. 32
  3. 48
  4. 64

A
32
B
24
C
64
D
48
Solution
Verified by Toppr

f(x)=g(x) (given)
By multiply both sides with f(x), we get
f(x)f(x)=g(x)f(x) ...(1)
f(x)=g(x)
Eqn (1) becomes
f(x)f(x)=g(x)g(x)
Now integrating both sides, we get
f2(x)+g2(x)=c
Where, c is the constant of integration.
Now, it is given that f(2)=g(2)=4
c=32
f2(24)+g2(24)=32

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