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Example 26 - Let f(x) = 2x, g(y) = 3y + 4, h(z) = sin z - Examples

Example 26   - Chapter 1 Class 12 Relation and Functions - Part 2
Example 26   - Chapter 1 Class 12 Relation and Functions - Part 3

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Example 26 Consider f : N → N, g : N → N and h : N → R defined as f (x) = 2x, g (y) = 3y + 4 and h (z) = sin z, ∀ x, y and z in N. Show that ho(gof) = (hog)of. f(x) = 2x , g(y) = 3y + 4 & h(z) = sin z We have to prove ho(gof) = (hog)of Taking L.H.S ho(gof) gof = g(f(x)) = g(2x) = 3(2x) + 4 = 6x + 4 ho(gof) = h(6x + 4) = sin(6x + 4) Taking L.H.S (hog)of hog = h(g(x)) = h(3y + 4) = sin(3y + 4) Let hog = p(y) Now (hog)of = pof = p(f(x)) = p(2x) = sin(3(2x) + 4) = sin(6x + 4) = ho(gof) = L.H.S Since L.H.S = R.H.S Hence proved

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.