# If f(x) = x2 – 3x + 4, then find the values of x satisfying the equation f(x) = f(2x + 1).

Given f(x) = x2 – 3x + 4.

We need to find x satisfying f(x) = f(2x + 1).

We have f(2x + 1) = (2x + 1)2 – 3(2x + 1) + 4

f(2x + 1) = (2x)2 + 2(2x)(1) + 12 – 6x – 3 + 4

f(2x + 1) = 4x2 + 4x + 1 – 6x + 1

f(2x + 1) = 4x2 – 2x + 2

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

x2 – 3x + 4 = 4x2 – 2x + 2

3x2 + x – 2 = 0

3x2 + 3x – 2x – 2 = 0

3x(x + 1) – 2(x + 1) = 0

(x + 1)(3x – 2) = 0

x + 1 = 0 or 3x – 2 = 0

x = –1 or 3x = 2

x = –1 or

Thus, the required values of x are –1 and.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Trigonometric Functions - 0568 mins
Trigonometric Functions - 0152 mins
Conditional IdentitiesFREE Class
Trigonometric Functions - 0658 mins
Questions Discussion of BiomoleculesFREE Class
Trigonometric Functions - 0366 mins
Let's Play the Game of Inequalities52 mins
Trigonometric Functions - 0865 mins
Trigonometric Functions - 0760 mins
Master Solving Problems of trigonometry45 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses