Question

Is g = {(1, 1), (2, 3), (3, 5), (4, 7)} a function from A = {1, 2, 3, 4} to B = {1, 3, 5, 7}? If this is given by the formula g(x) = ax + b then find a and b.

Answer 1

Answer:

a = 2, b = -1

Step-by-step explanation:

Given: g = {(1,1),(2,3),(3,5),(4,7)}

Each element of domain has unique image.So,g is a function.

Given that g(x) = ax + b

(i) For (1,1):

1 = a(1) + b

1 = a + b.

(ii) For(2,3):

3 = a(2) + b

3 = 2a + b

On solving (i) & (ii), we get

a + b = 1

2a + b = 3

--------------

-a = -2

a = 2

Substitute a = 2 in (i), we get

a + b = 1

2 + b = 1

b = -1.

Therefore, the values of a and b are 2,-1.

Hope it helps!

Answer 2

Answer:

a = 2 , b = -1

Step-by-step explanation:

In the attachment I have answered this problem.

See the attachment for detailed solution.

I hope this answer helps you