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Let A = { x ∈ R : x ≠ 0, − 4 ≤ x ≤ 4 } and f : A → R is defined by f (x)   = | x |/x for x ∈ A . Then the range of f is
  • a)
    {1, -1}
  • b)
    { x : 0 ≤ x ≤ 4 }
  • c)
    {1}
  • d)
    { x : − 4 ≤ x ≤ 0 }
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
Let A = { x ∈ R : x ≠ 0, − 4 ≤ x ≤ 4 } and f : A &...
Explanation:

Domain of the function f:
- The function f is defined for x ∈ A where A = { x ∈ R : x ≠ 0, -4 ≤ x ≤ 4 }.
- This means f is defined for all real numbers x except 0 within the interval [-4, 4].

Definition of the function f(x):
- The function f(x) = |x|/x for x ∈ A.
- When x is positive, f(x) = |x|/x = x/x = 1.
- When x is negative, f(x) = |x|/x = -x/x = -1.

Range of the function f:
- Since f(x) can only take the values 1 or -1 depending on the sign of x, the range of f is {1, -1}.
- So, the correct answer is option 'A' which states the range as {1, -1}.
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Let A = { x ∈ R : x ≠ 0, − 4 ≤ x ≤ 4 } and f : A → R is defined by f (x) = | x |/x for x ∈ A . Then the range of f isa){1, -1}b){ x : 0 ≤ x ≤ 4 }c){1}d){ x : − 4 ≤ x ≤ 0 }Correct answer is option 'A'. Can you explain this answer?
Question Description
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