Question

Let f: R→R be a function defined as f(x) = x^2/(1-x^2),where x∈ R. Find
A) Domain of the function?
B) Co domain of the function?
C ) Range of function​

Answer 1

Answer:

What would you like to ask?

12th

Maths

Relations and Functions

Types of Functions

Classify the following func...

MATHS

avatar

Asked on November 22, 2019 by

Kanti Brar

Classify the following function as injection, surjection or bijection:

f:R→R given by f(x)=sinx

MEDIUM

Help best friend

Study later

ANSWER

Injectivetest:

x

1

and x

2

are elements in domain (R) such that,

f(x

1

)=f(x

2

)

⇒ sinx

1

=sinx

2

Here, x

1

may not be equal to x

2

because sin0=sinπ.

So, 0 and π have same image 0.

∴ f is not an injective.

Surjectivetest:

y be the element in domain (R) such that,

f(x)=y

⇒ sinx=y

⇒ x=sin

−1

(y)

Now, for y>1, x∈

/

R ( Domain )

∴ f not surjective.

Bijectivetest:

f is not injective and surjective , then it is not bijective.