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Question

If f(x)=4xx2, xϵR, then write the value of f(a + 1) - (a - 1).

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Solution

We have,
f(x)=4xx2
Now,
f(a+1)=4(a+1)(a+1)2=4a+4a212a=a2+3+2af(a+1)=a2+2a+3
and,
f(a1)=4(a1)(a1)2=4a4(a2+12a)=4a4a21+2a=6aa25f(a1)=a2+6a5(ii)
Subtracting equation (ii) from equation (i), we get
f(a+1)f(a1)=a2+2a+3(a2+6a5)=a2+2a+3+a26a+5=4a+8=4(2a)


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