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Definition of Functions

Let fx be a...

Question

Let $f (x)$ be a polynomial with integer coefficients satisfying $f (1) = 5$ and $f (2) = 7$ . The smallest possible positive value of $f (12)$ is

5

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7

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27

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15

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Solution

The correct option is C $27$
$f (12)$ will have the smallest value if the degree of polynomial is minimum.
Let $f (x)$ be $2 x + 3$ , which satisfies $f (1) = 5$ and $f (2) = 7$
Therefore, minimum value of $f (12)$ $= (2 \times 12) + 3 = 27$

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Similar questions

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Let f(x) be a polynomial with integer coefficients satisfying f(1)=5 and f(2)=7. The smallest possible positive value of f(12) is

The correct option is C 27f(12) will have the smallest value if the degree of polynomial is minimum.Let f(x) be 2x+3, which satisfies f(1)=5 and f(2)=7Therefore, minimum value of f(12) =(2×12)+3=27

Let $f (x)$ be a polynomial with integer coefficients satisfying $f (1) = 5$ and $f (2) = 7$ . The smallest possible positive value of $f (12)$ is

The correct option is C $27$
$f (12)$ will have the smallest value if the degree of polynomial is minimum.
Let $f (x)$ be $2 x + 3$ , which satisfies $f (1) = 5$ and $f (2) = 7$
Therefore, minimum value of $f (12)$ $= (2 \times 12) + 3 = 27$