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Q) f: R--- R is a function satisfying f(2x+3) + f(2x+7) = 2 ( x belong to R) , then period of f(x):

(ans:4)

The given function is as,f2x+3+f2x+7=2                ....1Replace x by x+1 in equation 1,f2x+1+3+f2x+1+7=2⇒f2x+2+3+f2x+2+7=2⇒f2x+5+f2x+9=2             ....2Replace x by x+1 in equation 2,f2x+1+5+f2x+1+9=2⇒f2x+2+5+f2x+2+9=2⇒f2x+7+f2x+11=2           ....3Subtracting equation 1 and 3,f2x+3-f2x+11=0⇒f2x+3=f2x+11=f2x+4+3⇒Time Period T=4

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