Trying to find the right answer to this..

f(x) = x 2 – 3 x + 2 Replacing x by f (x). we get. f (f(x)) = ( f(x)) 2 –3 f(x) + 2 = (x 2 – 3 x + 2) 2 –3(x 2 – 3 x + 2) + 2 = x 4 + 9 x 2 + 4 – 6 x 3 – 12 x + 4 x 2 – 3 x 2 + 9 x – 6 + 2 = x 4 – 6 x 3 +10 x 2 – 3 x

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Relations and Functions

Short Answer Type

271.

Consider f : N → N, g : N → N and h : N → R defined as f (x) = 2 x, g(y) = 3 y + 4 and h(z) = sin z ∀ x, y and z in N. Show that h o (g o f) = (h o g) o f.

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272. Let f: (I, 2. 3} → a b. c be one-one and onto function given by f(I) = a,f(2) = b and f(3) = c. Show that there exists a function g : {a, b. c} → {1, 2, 3} such that g o f = 1_x and f o g = 1_Y where, X = {1, 2, 3} and Y= {a, b, c}.

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273.

Let f, g and h be function from R to R. Show that (f + g) o h = f o h + g o h

(f . g) o h = (f o h) . (g o h)

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274. Let f : Z → Z be defined by f (x) = x + 2. Find g : Z → Z such that gof = I_z.

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

f(x) = x² – 3 x + 2 Replacing x by f (x). we get.
f (f(x)) = ( f(x))² –3 f(x) + 2
= (x² – 3 x + 2)² –3(x² – 3 x + 2) + 2
= x⁴+ 9 x² + 4 – 6 x³ – 12 x + 4 x² – 3 x² + 9 x – 6 + 2 = x⁴ – 6 x³ +10 x² – 3 x