Let f(x) denote a polynomial of degree 3. Suppose $f (x + 2) - f (x) = x^{2} + 4 x + 4 a n d f (1) = 9.$ Find the value of f(3)

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Solution

The correct option is A
18

$f (x + 2) - f (x) = x^{2} + 4 x + 4 P u t x = 1 f (1 + 2) - f (1) = (1)^{2} + 4 (1) + 4 \Rightarrow f (3) - f (1) = 1 + 4 + 4 \Rightarrow f (3) = 9 + f (1) = 9 + 9 = 18$

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Let f(x) denote a polynomial of degree 3. Suppose f(x+2)−f(x)=x2+4x+4 and f(1)=9. Find the value of f(3)

The correct option is A 18 f(x+2)−f(x)=x2+4x+4Put x=1f(1+2)−f(1)=(1)2+4(1)+4⇒f(3)−f(1)=1+4+4⇒f(3)=9+f(1)=9+9=18

Let f(x) denote a polynomial of degree 3. Suppose $f (x + 2) - f (x) = x^{2} + 4 x + 4 a n d f (1) = 9.$ Find the value of f(3)

The correct option is A
18

$f (x + 2) - f (x) = x^{2} + 4 x + 4 P u t x = 1 f (1 + 2) - f (1) = (1)^{2} + 4 (1) + 4 \Rightarrow f (3) - f (1) = 1 + 4 + 4 \Rightarrow f (3) = 9 + f (1) = 9 + 9 = 18$