Answer:
Option D is correct. f(x) = |x - 2| + 1
Step-by-step explanation:
<em>Option A : f(x) = |x| + 1 </em>INCORRECT
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.
<em>Option B f(x) = | x-2 | </em>INCORRECT
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.
<em>Option C : f(x) = | x-2 | - 1 </em>INCORRECT
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.
<em>Option D : f(x) = | x-2 | + 1 </em>CORRECT
x = -2
f(-2) = |-2 - 2| + 1 = |-4| + 1 = 4 + 1 = 5
⇒f(-2) is equal to given value of f (-2).
x = 0
(0) = |0 - 2| + 1 = |-2| + 1 = 2 + 1 = 3
⇒f(0) is equal to given value of f (0).
x = 2
f(2) = |2-2| +1 = |0| + 1 = 0 + 1 = 1
⇒f(2) is equal to given value of f(2).
x = 3
we get, f(3) = |3-2| + 1 = |1| + 1 = 1 + 1 = 2
⇒f(3) is equal to given value of f(3).
x = 5
f(5) = |5 - 2| + 1 = |3| + 1 = 3 + 1 = 4
⇒f(5) is equal to given value of f(5).
Therefore, Option D is correct.
