Let a function f : R → R is defined such that 3f(2x^2 -3x + 5) + 2f(3x^2 -2x + 4)

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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

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