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Examples
Last updated at Jan. 28, 2020 by Teachoo
Example 16 Let f(x) = x2and g(x) = 2x + 1 be two real functions. Find (f + g) (x), (f β g) (x), (fg) (x), ("f" /π) (x) f(x) = x2 & g(x) = 2x + 1 (f + g) (x) = f(x) + g(x) = (x2) + (2x + 1) = x2 + 2x + 1, β΄(f + g) (x) = x2 + 2x + 1 (f β g) (x) = f(x) β g(x) = (x2) β (2x + 1) = x2 β 2x β 1 β΄ (f β g) (x) = x2 β 2x β 1 f(x) = x2 & g(x) = 2x + 1 (fg) (x) = f(x) Γ g(x) = x2 (2x + 1) = x2 (2x) + x2 (1) = 2x3 + x2, β΄ (fg) (x) = 2x3 + x2, (f/g) (x) = (f(x))/(g(x)) where, g (x) β 0, x β R = x2/(2x + 1) Example 16 Let f(x) = x2and g(x) = 2x + 1 be two real functions. Find (f + g) (x), (f β g) (x), (fg) (x), ("f" /π) (x) f(x) = x2 & g(x) = 2x + 1 (f + g) (x) = f(x) + g(x) = (x2) + (2x + 1) = x2 + 2x + 1, β΄(f + g) (x) = x2 + 2x + 1 (f β g) (x) = f(x) β g(x) = (x2) β (2x + 1) = x2 β 2x β 1 β΄ (f β g) (x) = x2 β 2x β 1 f(x) = x2 & g(x) = 2x + 1 (fg) (x) = f(x) Γ g(x) = x2 (2x + 1) = x2 (2x) + x2 (1) = 2x3 + x2, β΄ (fg) (x) = 2x3 + x2, (f/g) (x) = (f(x))/(g(x)) where, g (x) β 0, x β R = x2/(2x + 1) Where , 2x + 1 β 0 2x β 0 β 1 2x β β 1 x β (β1)/2 β΄ (π/π ) (x) = ππ/(ππ + π) , where x β (βπ)/π