Mathematics
Functions
Practice questions
If (f:(0,\infty)\to\mathbb{R}) is defined by (f(x)=\ln x), what is (f^{-1}(x))?If (f(x)=x^2-4x+7), what is its minimum value?If (f:\mathbb{R}\to[3,\infty)) is defined by (f(x)=x^2-4x+7), which statement is correct for (f)?If (f:A\to B) is a function, which situation violates the definition of a function?On the set (A={1,2,3}), (f={(1,2),(2,3),(3,1)}) is given. Which statement about (f) is correct?If (f={(1,2),(1,3),(2,4)}), why is this not a function?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=ax+b), when will (f) be one-one and onto?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=ax^2) with (a\neq0), why is (f) not one-one?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^3-3x), it is not one-one. Which example proves this correctly?If (f:A\to B) and (g:B\to A) satisfy (g\circ f=I_A), what conclusion about (f) is definitely true?If (f:A\to B) and (g:B\to A) satisfy (f\circ g=I_B), what conclusion about (f) is definitely true?If \(f:\mathbb{R}\setminus{0}\to\mathbb{R}\setminus{0}\) is defined by \(f(x)=\frac{1}{x}\), what is (f\circ f)?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=2x+3) and (g:\mathbb{R}\to\mathbb{R}) by (g(x)=\frac{x-3}{2}), which statement is correct?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^2), why does (f^{-1}) not exist as an ordinary function?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^2+2x), what is the range of (f)?If (f:\mathbb{R}\to\mathbb{R}) satisfies (f(x+1)=f(x)+2) and (f(0)=3), what is the value of (f(2))?If (f:\mathbb{R}\to\mathbb{R}) is an odd function and (f(4)=9), what is (f(-4))?If (f:\mathbb{R}\to\mathbb{R}) is an even function and (f(-6)=11), what is (f(6))?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^4+x^2), which statement about (f) is correct?If (f:\mathbb{R}\to\mathbb{R}) is defined by (f(x)=x^5-3x), what type of function is (f)?