Question

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

answer it correctly

Answer 1

Answer:

Given function:

f(x) = x2 − 3x + 2.

To find f(f(x))

f(f(x)) = f(x)2 − 3f(x) + 2.

= (x2 – 3x + 2)2 – 3(x2 – 3x + 2) + 2

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

= (x2)2 + (3x)2 + 22– 2x2 (3x) + 2x2(2) – 2x2(3x) – 3(x2 – 3x + 2) + 2

Now, substitute the values

= x4 + 9x2 + 4 – 6x3 – 12x + 4x2 – 3x2 + 9x – 6 + 2

= x4 – 6x3 + 9x2 + 4x2 – 3x2 – 12x + 9x – 6 + 2 + 4

Simplify the expression, we get,

f(f(x)) = x4 – 6x3 + 10x2 – 3x

Answer 2

Answer:

Given function:

f(x) = x2 − 3x + 2.

To find f(f(x))

f(f(x)) = f(x)2 − 3f(x) + 2.

= (x2 – 3x + 2)2 – 3(x2 – 3x + 2) + 2

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

= (x2)2 + (3x)2 + 22– 2x2 (3x) + 2x2(2) – 2x2(3x) – 3(x2 – 3x + 2) + 2

Now, substitute the values

= x4 + 9x2 + 4 – 6x3 – 12x + 4x2 – 3x2 + 9x – 6 + 2

= x4 – 6x3 + 9x2 + 4x2 – 3x2 – 12x + 9x – 6 + 2 + 4

Simplify the expression, we get,

f(f(x)) = x4 – 6x3 + 10x2 – 3x

Step-by-step explanation: