Answer :
Final answer:
The given function f(x)=e^(3x^2+1) is neither one-to-one nor onto. It is not one-to-one because it produces the same output for different inputs, and it is not onto because it can't produce negative outputs.
Explanation:
The function given is f(x)=e^(3x^2+1). In mathematics, a function is said to be one-to-one (1-1) if no two different input values result in the same output value, and it is onto if every possible output value is the result of an input value.
In this case, this particular function is not one-to-one because for any x value other than 0, there will be another negative x value that produces the same result. Example, f(1)=f(-1), i.e. it produces the same output for different inputs.
This function is also not onto because it is always positive due to the nature of exponential function and the fact that the e^(3x^2+1) can't produce negative results. Therefore, it cannot cover the whole set of real numbers.
So, option A - '1-1, not onto' is incorrect, and option B - 'onto, not 1-1' is also incorrect, but the function is neither 1-1 nor onto, which is not given as an option in your question.
Learn more about One-to-One and Onto Functions here:
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