Question

If $2f\left(x\right)+3f(-x)=x^2-x+1$, then the value of $f\left(1\right)$ is equal to

• A. $3/5$
• B. $4/5$
• C. $6/5$
• D. $7/5$

Answer 1

The correct option is D $7/5$

$2f\left(x\right)+3f(-x)=x^2-x+1$ ----- (i)

putting $x=1$ we get,

$2f\left(1\right)+3f(-1)=1$ ----- (ii)

putting $x=-1$ in (i) we get,

$2f(-1)+3f\left(1\right)=3$ ---- (iii)

multiplying (ii) by $2$ and (iii) by $3$

$4f\left(1\right)+6f(-1)=2$ ---- (iv)

$9f\left(1\right)+6f(-1)=9$ ---- (v)

subtracting (iv) from (v), we get

$5f\left(1\right)=7$

$f\left(1\right)=\frac{7}{5}$