Mathematics
Functions
Practice questions
If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are given by (f(x)=x+1), (g(x)=2x), which statement about ((f\circ g)(x)) and ((g\circ f)(x)) is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{x}{1+|x|}), what is the range of (f)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=2x^3-1), what is (f^{-1}(x))?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^2), why is (f^{-1}) not a function?If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x^2+4), what is the range of (f)?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=\cos x), why is (f) not onto?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^3-3x), why is (f) not one-one?If (f:\mathbb{R}\to(0,\infty)) is given by (f(x)=e^x), what type of function is (f)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=e^x), which statement is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\tan x), why is this function not well-defined?If (f:\mathbb{R}\setminus{-2}\to\mathbb{R}\setminus{3}) is given by (f(x)=\frac{3x+1}{x+2}), which value is missed by (f)?If (f:A\to A), (A={1,2,3}), and (f(1)=2), (f(2)=3), (f(3)=1), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=|x-2|), what is the minimum value of (f)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\lfloor x\rfloor), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x^2+ax+1) is one-one, which statement is correct?If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are both one-one, which statement about (g\circ f) is correct?If (f:A\to B) and (g:B\to C) are both onto, which statement about (g\circ f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{x+1}{x-1}), what are the domain and the missed range value of (f)?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=2x-5), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^2+1), why is this function not onto?