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Given f(x) = x – 2; g(x) = 3x + 5; h(x) = 2x – 3. Verify that (goh) of = go (hof)

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f(x) = x – 2 ; g(x) = 3x + 5; h(x) = 2x – 3

L.H.S. (goh) of

goh = g[h(x)]

= g(2x – 3)

= 3(2x – 3) + 5

= 6x – 9 + 5

= 6x – 4

(goh) of = goh [f(x)]

= goh (x – 2)

= 6(x – 2) – 4

= 6x – 12 – 4

= 6x – 16 … (1)

R.H.S. go(hof)

hof = h[f(x)]

= h(x- 2)

= 2(x – 2) – 3

= 2x – 4 – 3

= 2x – 7

go(hof) = g [hof (x)]

= g (2x – 7)

= 3(2x – 7) + 5

= 6x – 21 + 5

= 6x – 16 ... (2)

From (1) and (2) we get (goh)of = go(hof)

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