Paragraph: If f: R R and f(x)=g(x)+h(x) where g(x) is a polynomial and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is onto if g(x) is of odd degree and f(x) is into if g(x) is of even degree. To check w

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Paragraph: If f: R R and f(x)=g(x)+h(x) where g(x) is a polynomial and h(x) is a continuous and differentiable bounded function on both sides, then f(x) is onto if g(x) is of odd degree and f(x) is into if g(x) is of even degree. To check whether f(x) is one-one we need to differentiate f(x) . If f^ (x) changes sign in domain of f then f is many-one else one-one Question: f: R R and f(x)=a₁ x+a₃ x^3+a₅ x^5+ +a_ 2 n+1

Quantrex Academy · Accepted Answer

Correct answer: C. one-one onto

f(x)= odd degree polynomial + bounded function ⁻¹ x (0, ) also, f^ (x) 0 .

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