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(A) Given equation: $3f(2x^2 - 3x + 5) + 2f(3x^2 - 2x + 4) = x^2 - 7x + 9$ $\dots(1)$ To find $f(5)$,we observe the arguments of $f$. Case $1$: Put $x

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$\frac{21}{5}$

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(A) Given equation: $3f(2x^2 - 3x + 5) + 2f(3x^2 - 2x + 4) = x^2 - 7x + 9$ $\dots(1)$ To find $f(5)$,we observe the arguments of $f$. Case $1$: Put $x = 0$ in $(1)$: $3f(5) + 2f(4) = 9$ $\dots(2)$ Case $2$: Put $x = 1$ in $(1)$: $3f(2(1)^2 - 3(1) + 5) + 2f(3(1)^2 - 2(1) + 4) = 1^2 - 7(1) + 9$ $3f(4) + 2f(5) = 3$ $\dots(3)$ Now we have a system of two linear equations in $f(5)$ and $f(4)$: $3f(5) + 2f(4) = 9$ $2f(5) + 3f(4) = 3$ Multiply $(2)$ by $3$ and $(3)$ by $2$: $9f(5) + 6f(4) = 27$ $\dots(4)$ $4f(5) + 6f(4) = 6$ $\dots(5)$ Subtract $(5)$ from $(4)$: $(9f(5) - 4f(5)) = 27 - 6$ $5f(5) = 21$ $f(5) = \frac{21}{5}$

Let a function $f : R \rightarrow R$ be defined such that $3f(2x^2 - 3x + 5) + 2f(3x^2 - 2x + 4) = x^2 - 7x + 9$ for all $x \in R$. Then the value of $f(5)$ is:

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