Question

8.If f(x)=(x^(2)+2)/(x) then find the value of 2f(-1).​

Answer 1

f(x) -2f(1-x)=x^2+2 …..eq1

Putting x=y in above equation

f(y)-2f(1-y)=y^2+2 ……eq2

Putting x=1-y in first equation

f(1-y)-2f(1-[1-y])=(1-y)^2+2 .……eq3

Multiply by 2 in eq3 we get

2f(1-y)-4f(y)=2×(1-y)^2 +2×2 ……..eq4

Adding eq4 and eq2 we get

-3f(y)=y^2 +2+ 2×(1-y)^2 + 4

f(y)= —(3×y^2–4y+8)/3

Then put y=x again to have f(x)

f(x)= —(3×x^2–4x+8)/3