If f(x) = 4x – x2, x ∈ R, then write the value of f(a + 1) – f(a – InterviewSolution

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1.

If f(x) = 4x – x2, x ∈ R, then write the value of f(a + 1) – f(a – 1).

Answer»

f(x) = 4x – x²

f(a+1)-f(a-1) = [4(a+1) -(a+1)²] - [4(a-1)-(a-1)²]

= 4[(a+1) -(a-1)]- [ (a+1)² -(a+1)²]

= 4(2)-[(a+1+a-1) (a+1-a+1)]

Using : a² - b²= (a + b)(a-b)

f(a+1)-f(a-1)=4(2)-2a(2)

= 4(2-a)

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