Question

If f(x) + 3f(1/x) = 2x what is f(x)

Answer 1

Step-by-step explanation:

2f(x)+3f(−x)=x

2f(x)+3f(−x)=x 2

2f(x)+3f(−x)=x 2 −x+1 ----- (i)

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,2f(−1)+3f(1)=3 ---- (iii)

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,2f(−1)+3f(1)=3 ---- (iii)multiplying (ii) by 2 and (iii) by 3

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,2f(−1)+3f(1)=3 ---- (iii)multiplying (ii) by 2 and (iii) by 34f(1)+6f(−1)=2 ---- (iv)

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,2f(−1)+3f(1)=3 ---- (iii)multiplying (ii) by 2 and (iii) by 34f(1)+6f(−1)=2 ---- (iv)9f(1)+6f(−1)=9 ---- (v)

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,2f(−1)+3f(1)=3 ---- (iii)multiplying (ii) by 2 and (iii) by 34f(1)+6f(−1)=2 ---- (iv)9f(1)+6f(−1)=9 ---- (v)subtracting (iv) from (v), we get

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,2f(−1)+3f(1)=3 ---- (iii)multiplying (ii) by 2 and (iii) by 34f(1)+6f(−1)=2 ---- (iv)9f(1)+6f(−1)=9 ---- (v)subtracting (iv) from (v), we get5f(1)=7

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,2f(−1)+3f(1)=3 ---- (iii)multiplying (ii) by 2 and (iii) by 34f(1)+6f(−1)=2 ---- (iv)9f(1)+6f(−1)=9 ---- (v)subtracting (iv) from (v), we get5f(1)=7f(1)=

2f(x)+3f(−x)=x 2 −x+1 ----- (i)putting x=1 we get,2f(1)+3f(−1)=1 ----- (ii)putting x=−1 in (i) we get,2f(−1)+3f(1)=3 ---- (iii)multiplying (ii) by 2 and (iii) by 34f(1)+6f(−1)=2 ---- (iv)9f(1)+6f(−1)=9 ---- (v)subtracting (iv) from (v), we get5f(1)=7f(1)= 5/7

7

7

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