Question

f(x)=x^-3x+4 then values of x which satisfies f (1)+ f(x)= f(1)f(x)​

Answer 1

Answer:

f(x) = x² - 3x + 4

f(2x + 1) = (2x + 1)² - 3(2x + 1) + 4

= 4x² + 4x + 1 - 6x - 3 + 4

= 4x² + 2x + 2

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

x² - 3x + 4 = 4x² + 2x + 2

or, 4x² - x² + 2x + 3x + 2 - 4 = 0

or, 3x² + 5x - 2 = 0

or, 3x² + 6x - x - 2 = 0

or, 3x(x + 2) - 1(x + 2) = 0

or, (3x - 1)(x + 2) = 0

hence, x = -2 and 1/3