Most Important Selected Qs for JEE AdvancedMathematicsFunctions

If f(g(x)) is a one-one function, f: R R and g: R R , then

Options

Ag(x) must be one-one
Bf(x) must be one-one
Cf(x) may not be one-one
Dg(x) may not be one-one

Correct answer

C. f(x) may not be one-one

Step-by-step solution

Since f(g(x)) is a one-one function f ( g ( x ₁ ) ) f ( g ( x ₂ ) ) whenever x ₁ x ₂ g (x₁ ) g (x₂ ) whenever x₁ x₂ g ( x ) must be one-one. Let f(x)=y is satisfied by x=x₁ and x₂ If g(x) is such that its range has only one of x₁ and x₂ , then f(g(x)) can be one-one even if f(x) is many-one

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