Question

If f (x) = f (3x – 1) for f (x) = x2 – 4x +11, then x =

Answer 1

The first one is,

If f(x) =f (3x-1),

We may have, x =3x-1

So, we get

X= 1/2.

The second one is,

We have, f(x) =x^2-4x+11

Then, we get

x^2-4x +11= ( 3x-1)^2 -4 (3x-1)+11

Or, 4 (3x-1) -4x = (3x-1)^2 -x^2

Or, 4 ( 3x-1-x) = ( 3x-1-x)(3x-1+x)

Or, 4 (2x-1) =(2x-1)(4x-1)

Or, (2x-1)( 4-4x+1)=0

Either,

2x-1=0 ie x=1/2

Or,

5-4x=0 ie. X = 5/4

Hence, form the above two method we get two possible value for x.

They are 1/ 2 and 5/4.