Sir, you had given the answer that The range of f(x)=1+x^2+x^3 is the set of all values that f(x) can take .that is every element of codomain is related to element of domain is called Range.my question is that “At what value of x , f(x) =0 means Does 0Îrange has preimage  (x) in the domain ? “ Because you had written the range is -∞ To ∞ and 0Î(-∞,∞)

Asked by Kalyanrao Chavan | 2nd Jun, 2014, 06:25: PM

Expert Answer:

Let us observe the following graph:
The given graph passes through the y-axis at x=0 and the value of the function at x=0 is y=1.
Similarly, it passes through the x-axis at y=0 and the value of x is approximately, x = -1.45.
Thus, at x = -1.45, f(x) = 0.
I hope i have cleared your doubt to some extent.
If, not, please post your query once again.

Answered by Vimala Ramamurthy | 3rd Jun, 2014, 09:44: AM