Mathematics
Functions
Practice questions
If (A) has (n) elements, how many bijective functions are there from (A) to (A)?If (A={1,2,3}), how many functions from (A) to (A) are not one-one?If (A={1,2,3,4}) and (B={a,b}), how many functions from (A) to (B) are not onto?If \(f:\mathbb{R}\to\mathbb{R}\) is given by \(f(x)=\frac{x}{1+x^2}\), what is the range of (f)?Which of the following functions \(f:\mathbb{R}\to\mathbb{R}\) is one-one but not onto?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^3-6x^2+12x+1), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\begin{cases}2x+1,&x<1\x^2+2,&x\geq1\end{cases}), which statement about the range of (f) is correct?If (f:\mathbb{R}\setminus{1}\to\mathbb{R}\setminus{2}) is given by (f(x)=\frac{2x+3}{x-1}), what is the value of (f^{-1}(5))?If (A={1,2,3}) and (B={4,5}), how many functions can be formed from (A) to (B)?If (A) has (4) elements and (B) has (3) elements, how many one-one functions are possible from (A) to (B)?Choose the correct statement about the function (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+1).For (f:\mathbb{R}\to\mathbb{R}), (f(x)=3x-5), what is (f^{-1}(x))?If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3), what type of function is (f)?Which statement is correct for (f:\mathbb{R}\to[0,\infty)), (f(x)=x^2)?If (f:\mathbb{R}\to\mathbb{R}), (f(x)=|x|), what type of function is (f)?If (f:A\to B) is bijective and (|A|=7), what is the value of (|B|)?If (f(x)=2x+1) and (g(x)=x^2), what is ((g\circ f)(x))?If (f(x)=x+2) and (g(x)=3x-1), what is the value of ((f\circ g)(x)-(g\circ f)(x))?What is the range of (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2-4x+7)?Which statement is correct for (f:\mathbb{R}\to\mathbb{R}), (f(x)=5-2x)?