Let f : {2, 3, 4, 5} → {3, 4, 5, 9} and g : {3, 4, 5, 9} → {7, 11, 15} be functions defined as f(2) = 3, f(3) = 4, f(4) = f(5) = 5 and g (3) = g (4) = 7 and g (5) = g (9) = 11. Find gof.

Question

TextComposition of Functions

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Let y = f(1/x) and f′(x) = x³. What is the value of dy/dx at x = 1/2 ?

Find gof and fog, if f : R → R and g : R → R are given by f(x) = cos x and g (x) = 3x2. Show that gof ≠ fog.