Question

a function f is defined by f(x)=3-2x. Find 'x' if f(x²)=(f(x))².​

Answer 1

The function is defined as,

$\longrightarrow f(x)=3-2x\quad\quad\dots(1)$

Replacing $x$ by $x^2$ we get,

$\longrightarrow f(x^2)=3-2x^2$

Squaring (1) we get,

$\longrightarrow f^2(x)=(3-2x)^2$

$\longrightarrow f^2(x)=9-12x+4x^2$

As per the question,

$\longrightarrow f(x^2)=f^2(x)$

$\longrightarrow 3-2x^2=9-12x+4x^2$

$\longrightarrow9-12x+4x^2-3+2x^2=0$

$\longrightarrow6x^2-12x+6=0$

$\longrightarrow x^2-2x+1=0$

$\longrightarrow(x-1)^2=0$

$\Longrightarrow\underline{\underline{x=1}}$

Hence 1 is the answer.