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If y=f(x) satisfies f(x+1)+f(z-1)=f(x+z) x, z R and f(0)=0 and f^ (0)=4 then f(2) is equal to ______.

Correct answer

8

Step-by-step solution

aligned & Putting X=x+1 and Z=z+1 & f(X)+f(Z)=f(X+Z) & f^ (X)= _ h 0 f(X+h)-f(X) h = _ h f(X)+f(h)-f(X) h = _ h 0 f(h)-f(0) h & =f^ (0)=4 f^ (X)=4 f(X)=4 X+c & f(x)=4 x f(2)=8 aligned

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