If f(2x) + 3f(1/2x) = x+1 and x≠0 , then the value of 4f(2) equals
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Here, f(2x) + 3f(1/2x) = x + 1
f(2x) +3f(1/2x) = 2x/2 + 1
Take 2x = P
f(P) + 3f(1/P) = P/2 + 1 -----(1)
Now, Put P = 1/P
f(1/P) + 3f(P) = 1/2P + 1 -----(2)
multiply 3 with equation (2) and then, subtracted (1) from it
3f(1/P) + 9f(P) - f(P) - 3f(1/P) = 3/2P + 3 - P/2 -1
8f(P) = 3/2P - P/2 + 2
Now, put P = 2x
8f(2x) = 3/4x - 2x/2 + 2 = 3x/4 - x + 2
put x = 1
8f(2) = 3/4 - 1 + 2 = 3/4 + 1 = 7/4
Hence, f(2) = 7/32
f(2x) +3f(1/2x) = 2x/2 + 1
Take 2x = P
f(P) + 3f(1/P) = P/2 + 1 -----(1)
Now, Put P = 1/P
f(1/P) + 3f(P) = 1/2P + 1 -----(2)
multiply 3 with equation (2) and then, subtracted (1) from it
3f(1/P) + 9f(P) - f(P) - 3f(1/P) = 3/2P + 3 - P/2 -1
8f(P) = 3/2P - P/2 + 2
Now, put P = 2x
8f(2x) = 3/4x - 2x/2 + 2 = 3x/4 - x + 2
put x = 1
8f(2) = 3/4 - 1 + 2 = 3/4 + 1 = 7/4
Hence, f(2) = 7/32
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