Mathematics
Functions
Practice questions
If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=ax+b), when is (f) invertible?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=|x|), which statement is correct?If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=x^3), what is the value of (f^{-1}(8))?If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are given by (f(x)=2x+1), (g(x)=x^2-1), what is ((f\circ g)(x))?If (f:\mathbb{N}\to\mathbb{N}) is given by (f(n)=n+1), which statement about (f) is correct?If (f:\mathbb{Z}\to\mathbb{Z}) is defined by (f(x)=x+2), what type of function is (f)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{1}{1+x^2}), what is the range of (f)?If (f:\mathbb{R}\setminus{0}\to\mathbb{R}\setminus{0}) is given by (f(x)=\frac{1}{x}), what is (f^{-1}(x))?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^2-4x+7), what is the minimum value of (f)?If (f:A\to B) is onto, (|A|=3), and (|B|=4), which statement is correct?If (f:\mathbb{R}\to\mathbb{R}) and (f(x)=kx+7) is not one-one, what is the value of (k)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^5+x), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^4), which statement is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=3x-2) and (g:\mathbb{R}\to\mathbb{R}) by (g(x)=\frac{x+2}{3}), what is the relation between (g) and (f)?If (f:A\to B), (A={1,2,3}), and (B={4,5,6,7}), how many one-one functions are there?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\sin x), which statement about (f) is correct?If (f:[0,\infty)\to[0,\infty)) is defined by (f(x)=x^2), what type of function is (f)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^2-2x), what is the range of (f)?If (f(x)=\frac{x-1}{x+1}), what is the domain of (f)?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=5), which statement about (f) is correct?