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प्रश्न
If f(x) = 4x − x2, x ∈ R, then write the value of f(a + 1) −f(a − 1).
उत्तर
Given:
f(x) = 4x − x2, x ∈ 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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