Question

A function f is defined by f(x) = 3 - 2x . Find e such that f(x²) = (f(x))²​

Answer 1

Step-by-step explanation:

$\huge \underline{ \color{lime} \tt \color{red}Solution}$

$\sf f(x) = 3 - 2x$

$\sf f( {x}^{2} ) = 3 - {2x}^{2}$

$\sf \big[f(x) {\big]}^{2} = (3 - 2x {)}^{2}$

$\sf \implies \: \: \: \: \: \: \: \: \: 9 - 12x + {4x}^{2}$

$\sf 3 - {2x}^{2} = 9 - 12x + {4x}^{2}$

$\sf {4x}^{2} + {2x}^{2} - 12x + 9 - 3 = 0$

$\sf {6x}^{2} - 12x + 6 \div = \div 6$

$\sf {x}^{2} - 2x + 1 = 0$

$\sf {x}^{2} - 1x - 1x + 1 = 0$

$\sf x(x - 1) - 1(x - 1) = 0$

$\sf (x - 1)(x - 1) = 0$

$\large \fbox{ \sf \color{lime}x = 1 }$