Mathematics
Reflexive relation
Practice questions
If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^3-3x), choose the correct statement about (f) being onto.The function (f:\mathbb{R}\to(-\infty,4]) is defined by (f(x)=4-(x-2)^2). What type of function is it?If (f:[1,\infty)\to[0,\infty)) where (f(x)=x^2-2x+1), which option is correct for (f)?Let (f:\mathbb{R}\to(0,\infty)) where (f(x)=e^x). Which statement is correct about (f)?Why is \(f:\mathbb{R}\to\mathbb{R}\), where \(f(x)=e^x\), not onto?If (f:\mathbb{R}\to[-1,1]) where (f(x)=\sin x), what is the correct statement about (f)?The function \(f:\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\to[-1,1]\), where \(f(x)=\sin x\), is of which type?If (f:[0,\pi]\to[-1,1]), where (f(x)=\cos x), which statement is correct about (f)?Why is \(f:\mathbb{R}\to\mathbb{R}\), where \(f(x)=\tan^{-1}x\), not onto?If \(f:\mathbb{R}\to\left(-\frac{\pi}{2},\frac{\pi}{2}\right)\), where \(f(x)=\tan^{-1}x\), what is the correct conclusion?Is the function (f:\mathbb{Z}\to\mathbb{Z}), where (f(n)=2n+1), onto or not?If (f:\mathbb{Z}\to{y\in\mathbb{Z}:y\text{ is odd}}), where (f(n)=2n+1), what type is (f)?Why is (f:\mathbb{N}\to\mathbb{N}), where (f(n)=n+3), not onto?If (f:\mathbb{N}\to{n\in\mathbb{N}:n\ge4}), where (f(n)=n+3), choose the correct statement about (f).Let (A={1,2,3}), (B={a,b,c,d}). Is an onto function from (A) to (B) possible?If both (A) and (B) have (4) elements, how many onto functions are there from (A) to (B)?If (A) has (3) elements and (B) has (2) elements, choose the number of onto functions from (A) to (B).Let (f:A\to B) be onto and (g:B\to C) be onto. What is correct about (g\circ f:A\to C)?If (g\circ f:A\to C) is onto, what conclusion about (g:B\to C) is certain?If (g\circ f) is onto, which statement about (f) is not always true?