Question

If f(x) = x² – 3x + 4 and f(x) = f(2x + 1), find the values of x.

Answer 1

Given: f(x) = x² – 3x + 4 ----- (1) 

and f(x) = f(2x + 1)

Need to Find: Value of x

Replacing x by (2x + 1) in equation (1) we get,

f(2x + 1) = (2x + 1)² – 3(2x + 1) + 4 ----- (2)

According to the given problem, f(x) = f(2x + 1)

Comparing (1) and (2) we get,

x² – 3x + 4 = (2x + 1)² – 3(2x + 1) + 4

⇒ x² – 3x + 4 = 4x² + 4x + 1 – 6x – 3 + 4 

⇒ 4x² + 4x + 1 – 6x – 3 + 4 – x² + 3x – 4 = 0 

⇒ 3x² + x – 2 = 0 

⇒ 3x² + 3x – 2x – 2 = 0 

⇒ 3x(x + 1) – 2(x + 1) = 0 

⇒ (3x – 2)(x + 1) = 0 

So, either (3x – 2) = 0 or (x + 1) = 0

Therefore, the value of x is either 2/3 or -1