First slide

Functions (XII)

Question

$If f (x^{2} - 6 x + 6) + f (x^{2} - 4 x + 4) = 2 x \forall x \in R then f (- 3) + f (9) - 5 f (1) =$

Moderate

A

7
B

8
C

9
D

10

Solution

$Let x^{2} - 6 x + 6 = x^{2} - 4 x + 4$
Then x = 1
$Putting x = 1 in the given relation, we get f (1) = 1 .$
$\begin{array}{l} For x^{2} - 6 x + 6 = 1, x = 1 or 5 \\ For x^{2} - 4 x + 4 = 1, x = 1 or 3 \\ Put x = 3 and 5 in the given relation. \end{array}$
$\begin{array}{ll} f (- 3) + f (1) = 6 \Rightarrow f (- 3) = 5 \\ and f (1) + f (9) = 10 \Rightarrow f (9) = 9 \\ ∴ f (- 3) + f (9) - 5 f (1) = 9 \end{array}$

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