If f(x)= x2 -3x+4,then find the values of x satisfying the equation f(2x+1) - Maths - Relations and Functions

Question

If f(x)= x
2 -3x+4,then find the values of x
satisfying the equation f(2x+1)

Gursheen kaur. · Accepted Answer

If your question is: If f(x)= x 2 -3x+4, then find the values of x satisfying the equation f(x)= f(2x+1) Given: f(x) = x 2 â€“ 3x + 4 Now, replace x by 2x + 1, we get, $f (2 x + 1) = {(2 x + 1)}^{2} - 3 (2 x + 1) + 4 A s, f (x) = f (2 x + 1) ∴ x^{2} - 3 x + 4 = (2 x + 1)^{2} - 3 (2 x + 1) + 4 \Rightarrow x^{2} - 3 x + 4 = 4 x^{2} + 4 x + 1 - 6 x - 3 + 4 \Rightarrow x^{2} - 3 x + 4 = 4 x^{2} - 2 x + 2 o r x^{2} - 4 x^{2} - 3 x + 2 x + 4 - 2 = 0 \Rightarrow {3 x}^{2} + x - 2 = 0 \Rightarrow 3 x^{2} + 3 x - 2 x - 2 = 0 \Rightarrow 3 x (x + 1) - 2 (x + 1) = 0 \Rightarrow (x + 1) (3 x - 2) = 0 E i t h e r x + 1 = 0 o r 3 x - 2 = 0 \Rightarrow x = - 1 o r x = \frac{2}{3}$ Therefore, the value of x which satisfy the equation are â€“1 or $\frac{2}{3}$

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

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