Question

Find the domain and range of the function f(x)= √9-x² . OR. Let f = {(1,1) , (2,3) , (0,-1) , (-1,-3) } be a function from Z to Z defined by f(x) = ax+b , for som
e integers a, b. Determine a, b.​

Answer 1

Given : f(x)= √9-x²  

To Find : domain and range of the function

Solution:

f(x)= √9-x²  

=> 9-x² ≥ 0

=>  9  ≥ x²

=> x ² ≤ 9

=> x  ≤  | 3 |

=>  -3  ≤ x ≤ 3

Domain = [ - 3 , 3 ]

x = 3  ,  f(x) = 0

x = - 3 f(x) = 0

x = 0  f(x) = √9  = 3

Range  =  [0 , 3 ]

f = {(1,1) , (2,3) , (0,-1) , (-1,-3) }

f(x) = ax + b

=> 1 = a + b

- 1= 0 + b  => b = -1

1 = a - 1

=> a = 2

f(x) = 2x  - 1

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