Algebra

Relations & Functions

Medium

If $f:\mathbb{R} \to [-5, \infty)$ is defined as $f(x) = x^2 - 5$ , then the function f is

A. one-one

B. many-one

C. onto

D. into

Which of the above statements are true?

Choose the correct answer from the options given below:

A and C only

B and D only

B and C only

C and D only

✅ Correct Option: 3

Since $f(1) = -4 = f(-1)$ , $f$ is many-one (B). Range of $f$ is $[-5, \infty)$ , which equals the codomain, so $f$ is onto (C). So B and C are true.

2022: 6 Aug Shift 2

Match List I with List II

List I	List II
A. Range of $\lvert x\rvert$	I. $(-5, \infty)$
B. Range of $9x^2 + 6x - 5$ for all $x \geq 0$	II. $[0, \infty)$
C. Domain of $\dfrac{1}{\sqrt{x+5}}$	III. $\{(1,1), (2,2), (3,3)\}$
D. Smallest equivalence relation on Set $\{1,2,3\}$	IV. $[-5, \infty)$

Choose the correct answer from the options given below:

2026: 21 May Shift 1

The number of symmetric relations on set $A = \{1,2,3\}$ is

2026: 15 May Shift 1

If $A$ be the set of all real numbers and R be the relation on A defined by $R = \{(a,b): a^2+b^2=1, \forall a,b \in A\}$ , then R is

2026: 12 May Shift 2

Let $A$ be set of all real numbers and $R$ be a relation on $A$ defined by $R=\{(a,b): 1+ab>0\}$ , then relation $R$ is

2022: 25 May Shift 1

If $f: R \to R$ is defined by $f(x) = \sin x + x$ , then $f(f(x))$ is:

2025: 13 May Shift 1

Let $f: \mathbb{R}$ -> $\mathbb{R}$ be a function defined as $f(x) = x^4$ . Which one of the following is true?

If f:R→[−5,∞)f:\mathbb{R} \to [-5, \infty)f:R→[−5,∞) is defined as f(x)=x2−5f(x) = x^2 - 5f(x)=x2−5, then the function f is A. one-one B. many-one C. onto D. into Which of the above statements are true? Choose the correct answer from the options given below: