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Which of the given function is linear?*f (x) = | 3x – 1|f(x) = 2/(x + 7)f(x) = √x - 4f(x) = 2x/3

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Solution

The function that is linear among the given functions is f(x) = 2x/3.

Here's why:

  1. f (x) = | 3x – 1|: This is an absolute value function, not a linear function. A linear function is of the form y = mx + c, where m and c are constants. The absolute value function does not fit this form.

  2. f(x) = 2/(x + 7): This is a rational function, not a linear function. The denominator has a variable, which is not the case in a linear function.

  3. f(x) = √x - 4: This is a square root function, not a linear function. The variable is under a square root, which is not the case in a linear function.

  4. f(x) = 2x/3: This is a linear function. It is of the form y = mx + c, where m = 2/3 and c = 0.

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