Mathematics
Reflexive relation
Practice questions
Let (f:\mathbb{R}\to\mathbb{R}), where (f(x)=ax+b). What is the necessary and sufficient condition for (f) to be onto?If (f:\mathbb{R}\to\mathbb{R}), where (f(x)=k x^2+1), under which condition can (f) be onto?Is (f:\mathbb{R}\to[2,\infty)), where (f(x)=x^2+2), onto?If (f:[0,\infty)\to\mathbb{R}), where (f(x)=\sqrt{x}), why is (f) not onto?The function (f:[0,\infty)\to[0,\infty)), where (f(x)=\sqrt{x}), is of which type?If (f:\mathbb{R}\setminus{0}\to\mathbb{R}\setminus{0}), where (f(x)=\frac{1}{x}), choose the correct statement about (f).Is (f:\mathbb{R}\setminus{-1}\to\mathbb{R}\setminus{1}), where (f(x)=\frac{x}{x+1}), onto?If (f:\mathbb{R}\setminus{-1}\to\mathbb{R}), where (f(x)=\frac{x}{x+1}), why is it not onto?Is \(f:\mathbb{R}\to(0,1)\), where \(f(x)=\frac{1}{1+e^{-x}}\), onto or not?If (f:\mathbb{R}\to[0,1]), where (f(x)=\frac{1}{1+e^{-x}}), what is the correct conclusion?Let (f:\mathbb{R}\to[-1,\infty)), where (f(x)=x^2+2x). Which statement is correct about (f)?If (f:[-1,\infty)\to[-1,\infty)), where (f(x)=x^2+2x), is it onto or not?Why is (f:\mathbb{R}\to\mathbb{R}), where (f(x)=|x|+x), not onto?If (f:\mathbb{R}\to[0,\infty)), where (f(x)=|x|+x), is (f) onto or not?Let (f:\mathbb{R}\to[0,\infty)), where (f(x)=|x-3|). Is (f) onto?Why is (f:\mathbb{R}\to\mathbb{R}), where (f(x)=|x-3|), not onto?If (f:\mathbb{R}\to\mathbb{R}), where (f(x)=x^3+1), which statement is correct for (f)?What is the correct reason that (f:\mathbb{R}\to\mathbb{R}), where (f(x)=x^3+x), is onto?If (f:\mathbb{R}\to\mathbb{R}), where (f(x)=x^4+x^2), why is (f) not onto?Is (f:\mathbb{R}\to[0,\infty)), where (f(x)=x^4+x^2), onto?