Question

If f : R → R is defined by f(x) = x2 – 3x + 2, find f (f(x)).

Answer 1

f(x) = $x^2-3x+2$

f[f(x)] = $(x^2-3x+2)^2-3x+2$

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

= $x^4 -6x^3 + 13x^2 - 15x +6$

Answer 2

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Given function:

f(x) = x2 − 3x + 2.

To find f(f(x))

f(f(x)) = f(x)√2 − 3f(x) + 2.

= (x^2 – 3x + 2)^2 – 3(x^2 – 3x + 2) + 2

By using the formula (a-b+c)2 = a2+ b2+ c2-2ab +2ac-2ab, we get

= (x^2)^2 + (3x)^2 + 22– 2x^2 (3x) + 2x^2(2) – 2x^2(3x) – 3(x^2 – 3x + 2) + 2

Now, substitute the values

= x^4 + 9x^2 + 4 – 6x^3 – 12x + 4x^2 – 3x^2 + 9x – 6 + 2

= x^4 – 6x^3 + 9x^2 + 4x^2 – 3x^2 – 12x + 9x – 6 + 2 + 4

Simplify the expression, we get,

f(f(x)) = x^4 – 6x^3 + 10x^2 – 3x

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Hope It's Helpful.....:)