Mathematics
Functions
Practice questions
If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x|x|), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x|x|), what is (f^{-1}(4))?If (f:A\to B) and (g:B\to C), and (g\circ f) is one-one, which conclusion is definitely true?If (f:A\to B) and (g:B\to C), and (g\circ f) is onto, which conclusion is definitely true?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{x^2-1}{x-1}), on which domain does it behave like (x+1)?If (f:\mathbb{R}\setminus{1}\to\mathbb{R}) is given by (f(x)=\frac{x^2-1}{x-1}), what is the range of (f)?If (f:\mathbb{R}\to\mathbb{R}) is (f(x)=x^2+1) and (g:[1,\infty)\to\mathbb{R}) is (g(x)=\sqrt{x-1}), which statement is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\lfloor x\rfloor+{x}), where ({x}) is the fractional part, what is (f(x)) equal to?If (f:\mathbb{R}\to\mathbb{Z}) is given by (f(x)=\lfloor x\rfloor), which statement about (f) is correct?If (f:\mathbb{Z}\to\mathbb{Z}) is given by (f(n)=2n+1), which statement about (f) is correct?If (f:\mathbb{Z}\to\mathbb{Z}) is defined by (f(n)=n^3), which statement about (f) is correct?If (f:\mathbb{N}\to\mathbb{N}) is given by (f(n)=n^2), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\ln(1+x^2)), what is the range of (f)?If (f:(0,\infty)\to\mathbb{R}) is defined by (f(x)=\ln x), what type of function is (f)?If (f:\mathbb{R}\to(0,\infty)) is given by (f(x)=e^{2x+1}), what is (f^{-1}(x))?If \(f:\mathbb{R}\to\mathbb{R}\) is given by \(f(x)=\sin x+\cos x\), what is the range of (f)?If \(f:\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\to[-1,1]\) is given by \(f(x)=\sin x\), which statement about (f) is correct?If (f:[0,\pi]\to[-1,1]) is given by (f(x)=\cos x), what is (f^{-1}(0))?If (f:A\to B) is a function and (f^{-1}) is also a function, which statement about (f) is definitely true?If (f:A\to B) is bijective and (A) has (6) elements, how many elements does (B) have?