Consider the following statements : I. f is one-one function. II. f is onto function if the codomain is the set of natural numbers. Which of the statements given above is/are correct?
Consider the following for the two (02) items that follow : Let f=\{(1,1), (2, 4), (3, 7), (4, 10)\}.
- A. I only ✓
- B. II only
- C. Both I and II
- D. Neither I nor II
Correct Answer: A. I only
Explanation
Statement I is true because each input maps to a distinct output. Statement II is false because the range \{1, 4, 7, 10\} is not equal to the entire set of natural numbers (codomain), so it is not onto.
Related questions on Calculus
- Let z=[y] and y=[x]-x, where [.] is the greatest integer function. If x is <strong>NOT</strong> an integer but positive, then what i...
- If f(x)=4x+1 and g(x)=kx+2 such that fog(x)=gof(x), then what is the value of k?
- What is the <strong>MINIMUM</strong> value of the function f(x)=\log_{10}(x^{2}+2x+11)?
- What is \int(x^{x})^{2}(1+\ln x)\,dx equal to ?
- What is \int e^{x}\{1+\ln x+x\ln x\}\,dx equal to?