Maths · One-one, into and onto functions
The function \rightarrow\left(\mathbf{0}, e^{5}\right] \) defined by =e^{x^{3}-3
The function \( \boldsymbol{f}:(-\infty,-1) \rightarrow\left(\mathbf{0}, e^{5}\right] \) defined by \( f(x)=e^{x^{3}-3 x+2} \) is
- A. many-one and onto
- B. many-one and into
- C. one-one and onto
- D. one-one and into
Step-by-step solution
The function is strictly increasing on (-∞, -1) because the derivative of the exponent is positive, so it is one-one. The range is (0, e^4) which is a subset of the codomain (0, e^5], so it is into (not onto).
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