Question

Question 1. The function h is defined by h: x 6x +3 such that xe
R. Determine if h is
(a) surjective ​

Answer 1

Step-by-step explanation:

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.