Relations and F...

Let f: R → R be defined by f(x) = \(3x ^2\) - 5 and g: R → R by g(x) = \(x\over x^2+1\). Then gof is

Which of the following functions from Z into Z are bijections?

Let f: R → R be the functions defined by f(x) = \(x ^3\) + 5. Then \(f ^{-1}\)(x) is

Let f: A → B and g: B → C be the bijective functions. Then \((gof) ^{-1}\) is

Let f: R -\(\Big\{{3\over5}\Big\}\) → R be defined by f(x) = \(3x+2\over 5x-3\). Then

Let f: [0, 1] → [0, 1] be defined by \(f(x) = \begin{cases} x, & \quad \text{if } x \text{ is rational}\\ 1-x, & \quad \text{if } x \text{ is irrational} \end{cases}\) Then (\(fof\)) x is

Let f: [2, \(\infty\)) → R be the function defined by f(x) = \(x ^2 -4x + 5\), then the range of f is

Let f: N → R be the function defined by f(x) = \(2x-1\over 2\) and g: Q → R be another function defined by g(x) = x + 2. Then (gof)\((\frac{3}{2})\) is

Let f: R → R be defined by \(f(x) = \begin{cases} 2x :x>3 & \quad \\ x^2:1 < x \leq 3 & \quad \\3x : x \leq 1 \end{cases}\) Then f(-1) + f(2) + f(4) is

Let f: R → R be given by f(x) = tan x. Then \(f ^{-1}\) (1) is