Mathematics
Functions
Practice questions
If (f:\mathbb{R}\to\mathbb{R}), (f(x)=c), where (c) is a fixed real number, when will (f) be one-one?If (f:\mathbb{R}\to(0,\infty)), (f(x)=e^x), what type of function is (f)?Which statement is correct for (f:(0,\infty)\to\mathbb{R}), (f(x)=\ln x)?If (f(x)=\frac{x-1}{x+1}), then for (x\ne -1), what is (f^{-1}(x))?If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^3+x), what is the correct conclusion about (f)?If (f:A\to B) and (g:B\to C) are both one-one, what is true about (g\circ f)?Which statement is correct about (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^4)?If (f:[0,\infty)\to[0,\infty)), (f(x)=x^2), what is (f^{-1}(x))?If \(f(x)=\frac{1}{x}\), where (x\ne 0), what is the value of (f(f(x)))?If (f:\mathbb{R}\to\mathbb{R}), (f(x)=ax+b) is bijective, what is the necessary condition on (a)?If (f:\mathbb{R}\to\mathbb{R}), (f(x)=x^2+2x+2), what is the minimum value?If (f:\mathbb{R}\to[1,\infty)), (f(x)=x^2+1), which statement is correct about (f)?If (f:A\to B), where (A={1,2}), (B={a,b,c}), how many one-one functions are there from (A) to (B)?If (A) has (3) elements and (B) has (3) elements, how many bijective functions are possible from (A) to (B)?If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\sin x), what is the correct statement about (f)?What type is \(f:\left[-\frac{\pi}{2},\frac{\pi}{2}\right]\to[-1,1]\), \(f(x)=\sin x\)?If (f:\mathbb{R}\to\mathbb{R}), (f(x)=\cos x), which statement is correct?If \(f:\left[0,\pi\right]\to[-1,1]\), \(f(x)=\cos x\), what is the type of (f)?If (f(x)=2x+3) and (f^{-1}(k)=4), what is the value of (k)?If (f(x)=x^2-1) and (g(x)=x+1), what is the value of ((f\circ g)(2))?