Relation and Function Set-2

Q1. Let $f : R \rightarrow R$ be defined by $f(x) = 3x^2 – 5$ and $g : R \rightarrow R$ by $g(x) = \frac{2}{x^2 + 1}$ then $gof$ is

Q2. If the set $A$ contains 5 elements and set $B$ contains 6 elements, then the number of one-one and onto mapping from $A$ to $B$ is

Q3. Let $f : \rightarrow$ be defined by $f(x) = \{x, \text{ if } x \text{ is rational} ; 1-x, \text{ if } x \text{ is irrational}\}$. Then $(fof)x$ is

Q4. Let $f : [2, \infty) \rightarrow R$ be the function defined by $f(x) = x^2 – 4x + 5$, then the range of $f$ is

Q5. Let $f : R \rightarrow R$ be defined by $f(x) = \{2x^2 : x > 3; x^2 : 1 \leq x \leq 3; 3x : x < 1\}$. Then $f(– 1) + f(2) + f(4)$ is

Q6. The relation $R$ is defined on the set of natural numbers as $\{(a, b) : a = 2b\}$. Then, $R^{-1}$ is given by

Q7. Let $f : R \rightarrow R$ be a function defined by $f(x) = \frac{e^{|x|}-e^{-x}}{e^{x}+e^{-x}}$ then $f(x)$ is

Q8. Let $g(x) = x^2 – 4x – 5$, then

Q9. The function $f : R \rightarrow R$ given by $f(x) = x^3 – 1$ is

Q10. Let $f : [0, \infty) \rightarrow$ be defined by $f(x)=\frac{2 x}{1+x}$, then $f$ is

Q11. If $N$ be the set of all-natural numbers, consider $f : N \rightarrow N$ such that $f(x) = 2x, \forall x \in N$, then $f$ is

Q12. Let $A = \{x : -1 \leq x \leq 1\}$ and $f : A \rightarrow A$ is a function defined by $f(x) = x |x|$ then $f$ is

Q13. Let $f : R \rightarrow R$ be a function defined by $f(x) = x^3 + 4$, then $f$ is

Q14. If $f(x) = (ax^2 – b)^3$, then the function $g$ such that $f\{g(x)\} = g\{f(x)\}$ is given by

Q15. If $f : [1, \infty) \rightarrow [2, \infty)$ is given by $f(x) = x + \frac{1}{x}$, then $f^{-1}$ equals to