Mathematics
Functions
Practice questions
If (f:\mathbb{R}\setminus{2}\to\mathbb{R}\setminus{3}) is given by (f(x)=\frac{3x+1}{x-2}), what is (f^{-1}(x))?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=ax+b) and (f\circ f) is the identity function, which statement about (a,b) is correct?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^2-6x+11), what is the range of (f)?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=|x-1|+|x+1|), what is the range of (f)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\frac{x^2}{1+x^2}), what is the range of (f)?If (A) has (5) elements and (B) has (3) elements, how many functions from (A) to (B) have range exactly of size (2)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\begin{cases}x+2,&x\geq0\x^2+2,&x<0\end{cases}), which statement about (f) being one-one is correct?If (f:[0,\infty)\to\mathbb{R}) is given by (f(x)=x^2+2x), which statement about its range and one-one behaviour is correct?If (f:\mathbb{R}\to\mathbb{R}) is an odd function and (g:\mathbb{R}\to\mathbb{R}) is an even function, which statement about (g\circ f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is described by (f(x)=x+\frac{1}{x}), what should be the correct domain?If (f:(0,\infty)\to\mathbb{R}) is given by (f(x)=x+\frac{1}{x}), what is the range of (f)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=x^2+px+q) and its minimum value is (5) at (x=2), what are (p,q)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=mx^2+1), which value of (m) can make (f) one-one on all of (\mathbb{R})?If (f:\mathbb{R}\to\mathbb{R}) is considered as (f(x)=\frac{2x-1}{x+3}), which value must be removed from the domain to make it a function?If (f:\mathbb{R}\setminus{-3}\to\mathbb{R}\setminus{2}) is given by (f(x)=\frac{2x-1}{x+3}), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) and (g:\mathbb{R}\to\mathbb{R}) are (f(x)=x^2), (g(x)=x+1), what is ((f\circ g)(x)-(g\circ f)(x))?If (f:\mathbb{R}\to\mathbb{R}) satisfies (f(x+y)=f(x)f(y)), (f(0)=1), and (f(x)>0), what is (f(-x))?If (f:\mathbb{R}\to\mathbb{R}) satisfies (f(x+y)=f(x)+f(y)) and (f(1)=3), what is (f(5)), assuming (f) is linear?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\max{x,1-x}), what is the minimum value of (f)?If (f:\mathbb{R}\to\mathbb{R}) is given by (f(x)=\min{x^2,4}), what is the range of (f)?