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Example 17 - Let f(x) = root x, g(x) = x. Find f + g, fg, f/g

Example 17 - Chapter 2 Class 11 Relations and Functions - Part 2

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Example 17 Let f(x) = √π‘₯ and g(x) = x be two functions defined over the set of nonnegative real numbers. Find (f + g) (x), (f – g) (x), (fg) (x) and (𝑓/𝑔) (x) (f + g) (x) = f(x) + g(x) = √𝐱 + x, (f – g) (x) = f(x) – g(x) = √𝐱 – x (fg) x = f(x) Γ— g(x) = √x Γ— x = π‘₯^(1/2) Γ— x1 = π‘₯^(1/2+1) = π‘₯^((1+2)/2) = 𝒙^(πŸ‘/𝟐) (f/g) (x) = (f(x))/(g(x)) where, g (x) β‰  0, x ∈ R = √π‘₯/(x ) = √π‘₯/(√π‘₯ Γ—βˆšπ‘₯) = 1/√π‘₯ Where , √π‘₯ β‰  0 β‡’ x β‰  0 ∴ (𝐟/𝐠) (x) = 𝟏/βˆšπ’™ where x β‰  0

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