Answer:
Option D is correct.i.e., f(x) = | x - 2 | + 1
Explanation:
Function which satisfy the given data is our Ans.
So, we check for all functions.
Option A : f(x) = |x| + 1
put, x = -2
we get, f( -2 ) = |-2| + 1 = 2 + 1 = 3 ≠ 5
⇒f ( -2 ) is not equal to given value of f ( -2 ).
Thus, This is not function of given data.
Option B : f(x) = | x-2 |
put, x = -2
we get, f( -2 ) = | -2 - 2 | = | -4 | = 4 ≠ 5
⇒f ( -2 ) is not equal to given value of f ( -2 ).
Thus, This is not function of given data.
Option C : f(x) = | x-2 | - 1
put, x = -2
we get, f( -2 ) = | -2 - 2 | - 1 = | -4 | - 1 = 4 - 1 = 3 ≠ 5
⇒f ( -2 ) is not equal to given value of f ( -2 ).
Thus, This is not function of given data.
Option D : f(x) = | x-2 | + 1
put, x = -2
we get, f( -2 ) = | -2 - 2 | + 1 = | -4 | + 1 = 4 + 1 = 5
⇒f ( -2 ) is equal to given value of f ( -2 ).
put, x = 0
we get, f( 0 ) = | 0 - 2 | + 1 = | -2 | + 1 = 2 + 1 = 3
⇒f ( 0 ) is equal to given value of f ( 0 ).
put, x = 2
we get, f( 2 ) = | 2 - 2 | + 1 = | 0 | + 1 = 0 + 1 = 1
⇒f ( 2 ) is equal to given value of f ( 2 ).
put, x = 3
we get, f( 3 ) = | 3 - 2 | + 1 = | 1 | + 1 = 1 + 1 = 2
⇒f ( 3 ) is equal to given value of f ( 3 ).
put, x = 5
we get, f( 5 ) = | 5 - 2 | + 1 = | 3 | + 1 = 3 + 1 = 4
⇒f ( 5 ) is equal to given value of f ( 5 ).
Thus, This is function of given data.
Therefore, Option D is correct.