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If F(X) = 4x − X2, X ∈ R, Then Write the Value of F(A + 1) −F(A − 1). - CBSE (Science) Class 11 - Mathematics

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Question

If f(x) =  4x − x2x ∈ R, then write the value of f(a + 1) −f(a − 1).

 

Solution

Given:
f(x) =  4x − x2x ∈ R
Now,
f(a + 1) = 4(a + 1)  -(a + 1)2
             = 4a + 4 -(a2 + 1 + 2a)
             = 4a + 4 -a2 -1 - 2a 
             = 2a -a2 + 3
f(a -1) = 4(a -1) - 1) +1)2
             = 4a-4 - (a2 + 1 -2a)
             = 4a - 4 - a2 -1 + 2a 
             = 6a - a2 -5
Thus,
f(a + 1) − f(a − 1) = ( 2a -a2 + 3) -(6a -a2 -5)
                             = 2a -a2 + 3 -6a + a2 + 5
                             =  8 -4a
                             = 4(2 -a)

 
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APPEARS IN

 RD Sharma Solution for Mathematics Class 11 (2019 to Current)
Chapter 3: Functions
Ex.3.50 | Q: 10 | Page no. 41
Solution If F(X) = 4x − X2, X ∈ R, Then Write the Value of F(A + 1) −F(A − 1). Concept: Functions.
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