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Functions — Maths STD 11 Science — Question

CBSE BoardEnglish MediumSTD 11 ScienceMathsFunctions1 Mark
Question
If $\text{f(x)}=4\text{x}-\text{x}^2,\text{ x}\in\text{R},$ then write the value of $f(a + 1) - f(a - 1).$
✓

Answer

We have,
$f(x) = 4x - x^2$^
Now, $f(a + 1) = 4(a + 1) - (a + 1)^2$
$= 4a + 4 - a^2 - 1 - 2a$
$= -a^2+ 3 + 2a$
$\Rightarrow f(a + 1) = -a^2 + 2a + 3 ...(i)$
and, $f(a - 1) = 4(a - 1) - (a - 1)^2$
$= 4a - 4 - (a^2 + 1 - 2a)$
$= 4a - 4 - a^2 - 1 + 2a$
$= 6a - a - 5$
$f(a - 1) = -a^2 + 6a - 5 ....(ii)$
Subtracting equation (ii) from equation (i), we get
$f(a + 1) - f(a - 1)$
$= -a^2 + 2a + 3 - (-a^2 + 6a - 5)$
$= -a^2 + 2a + 3 + a^2 - 6a + 5$
$= -4a + 8 = 4(2 - a)$

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