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1.Relation and Function
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Let a function $f : R \rightarrow R$ is defined such that $3f(2x^2 -3x + 5) + 2f(3x^2 -2x + 4) = x^2 -7x + 9\ \ \ \forall x \in R$, then the value of $f(5)$ is-
A
$\frac{21}{5}$
B
$0$
C
$\frac{9}{5}$
D
$3$
Solution
$3 f\left(2 x^{2}-3 x+5\right)+2 f\left(3 x^{2}-2 x+4\right)=x^{2}-7 x+9$
Put $x=0 \quad 3 f(5)+2 f(4)=9 \quad \ldots(1)$
Put $x=1 \quad 3 f(4)+3 f(5)=3 \quad \ldots(2)$
Standard 12
Mathematics