Problem Solving

Que: If \(4f\left(x\right)-3f\left(-x\right)=2x-7\), what is the value of \(f\left(3\right)\)?

A) \(0\)

B) \(\frac{1}{7}\)

C) \(\frac{-43}{7}\)

D) \(\frac{36}{7}\)

E) \(\frac{43}{7}\)

Solution: 4f(x) - 3 f(-x) = 2x - 7 --------- equation (1)

Substituting x = 3 in equation (1)

=> 4f(3) - 3f(-3) = 2(3) - 7

=> 4f(3) - 3f(-3) = -1--------- equation (2)

Substituting x = -3 in equation (1)

=> 4f(-3) - 3f(3) = 2(-3) - 7

=> 4f(-3) - 3f(3) = -13--------- equation (3)

Multiplying equation (2) by ‘4’ we get,

=> 16f(3) - 12f(-3) = -4--------- equation (4)


Multiplying equation (3) by ‘3’ we get,

=> 12f(-3) - 9f(3) = -39--------- equation (5)

Adding Eqn(4) + Eqn(5)

=> 7f(3) = -43

=> f(3) = - \(\frac{43}{7}\)


C is the correct answer.

Answer C