Home » MCQs » Discrete Mathematics MCQs

# Discrete Mathematics | Identity and Composition of Functions MCQs

**Discrete Mathematics | Identity and Composition of Functions MCQs**: This section contains multiple-choice questions and answers on Identity and Composition of Functions in Discrete Mathematics.

Submitted by Anushree Goswami, on July 17, 2022

**1. When every element of set A has a copy of itself, it is called the identity function, f (a) = ___?**

- a ∀ A ∈ a
- A ∈ A
- a ∀ A ∈ A
- a ∀ a ∈ A

**Answer:** D) a ∀ a ∈ A

**Explanation:**

When every element of set A has a copy of itself, it is called the identity function, f (a) = a ∀ a ∈ A.

**2. Identity function is denoted by the symbol -?**

- ID
- I
- U
- T

**Answer:** B) I

**Explanation:**

Identity function is denoted by the symbol I.

**3. If f: X -> Y is a _____ function, it is invertible?**

- Dijective
- Discretive
- Bijective
- Bipolar

**Answer:** C) Bijective

**Explanation:**

If f: X -> Y is a bijective function, it is invertible.

**4. If f^-1 is a function from ___, there is an inverse function for f?**

- X to Y
- X to X
- Y to X
- Y to Y

**Answer:** C) Y to X

**Explanation:**

If f^-1 is a function from Y to X, there is an inverse function for f.

**5. g [f(x)] is known as -?**

- gox
- gof
- gfx
- gxf

**Answer:** B) gof

**Explanation:**

g [f(x)] is known as gof.

**6. _____ if f is A -> B and g is B -> C, which means composition of f with g is a function from A into C?**

- (gof) (y) = g [f(x)]
- (gof) (x) = g [f(y)]
- (gof) (x) = g [x(x)]
- (gof) (x) = g [f(x)]

**Answer:** D) (gof) (x) = g [f(x)]

**Explanation:**

(gof) (x) = g [f(x)] if f is A -> B and g is B -> C, which means composition of f with g is a function from A into C.

**7. It is necessary to ____ in order to find the composition of f and g?**

- find the image of f(x) under f before finding the image of f (x) under g
- find the image of x under f before finding the image of f (x) under f
- find the image of x under g before finding the image of f (x) under g
- find the image of x under f before finding the image of f (x) under g

**Answer:** D) find the image of x under f before finding the image of f (x) under g

**Explanation:**

It is necessary to find the image of x under f before finding the image of f (x) under g in order to find the composition of f and g.

**8. The function (gof) (gof) is _____ if f and g are one-to-one?**

- One-to-one
- One-to-many
- Many-to-one
- Many-to-many

**Answer:** A) One-to-one

**Explanation:**

The function (gof) (gof) is also one-to-one if f and g are one-to-one.

**9. Functions (gof) (gof) are onto if f and g are ___?**

- Into
- Onto
- To
- None

**Answer:** B) Onto

**Explanation:**

Functions (gof) (gof) are onto if f and g are onto.

**10. There is no commutative property in composition, but ____ property is present consistently?**

- Associative
- Identity
- Duplicative
- None

**Answer:** A) Associative

**Explanation:**

There is no commutative property in composition, but associative property is present consistently.

Comments and Discussions!