If f : R R is defined by f(x) = x 2 - 3x + 2 , find f(f(x)).

We are given that, f(x) = x 2 - 3x + 2 f[f(x)] = f( x 2 - 3x + 2) /[«] = /(x 2 - 3 * + 2) f[f(x)] = ( x 2 - 3x + 2) 2 - 3( x 2 - 3x + 2) + 2 = x 4 + 9 x 2 + 4 - 6 x 3 - 12x + 4 x 2 - 3 x 2 + 9x - 6 + 2 = x 4 - 6 x 3 + 10 x 2 - 3x. Hence, f(f(x)) = x 4 - 6x 3 + 10x 2 - 3x .

Relations and Functions — Class 12 Maths Solution

ncert misc SA NCERT Misc.,Q.3, Page 29

Question

If f : R $\rightarrow$ R is defined by f(x) $= x^2 - 3x + 2$, find f(f(x)).

Step-by-step Solution

We are given that, f(x) $= x^2 -$3x + 2

$\therefore$ $f[f(x)] = f({x^2} - 3x + 2)$ /[«] $= /(x^2 -$ 3$*$ + 2)

$\Rightarrow$ $f[f(x)] = {({x^2} - 3x + 2)^2} - 3({x^2} - 3x + 2) + 2$

$= {x^4} + 9{x^2} + 4 - 6{x^3} - 12x + 4{x^2} - 3{x^2} + 9x - 6 + 2$

$= {x^4} - 6{x^3} + 10{x^2} - 3x.$

Hence, f(f(x)) $= x^4 - 6x^3 + 10x^2 - 3x$.

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