Question

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

Answer 1

Question

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

Step-by-step explanation:

Given:

• f(x) = x2 – 3x + 4 ----- (1)
• f(x) = f(2x + 1)

To Find:

• Value of x

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

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

ATQ, f(x) = f(2x + 1)

Comparing (1) and (2) we get,

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

⇒ x^2 – 3x + 4 = 4x2 + 4x + 1 – 6x – 3 + 4

⇒ 4x^2 + 4x + 1 – 6x – 3 + 4 – x^2 + 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

So,x is either 2/x or -1.

$\large\cal{{@WildCat7083}}$

Answer 2

Answer:

X= -1, 2/3

Step-by-step explanation:

Solution Show Solution. Given: f (x) = x2 – 3x + 4. Therefore, f (2x + 1) ...