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e domain and range of the following functions:1. 𝑦 = 2𝑥 − 1

Question

e domain and range of the following functions:1. 𝑦 = 2𝑥 − 1

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Solution

  1. 𝑦 = 2𝑥 − 1

The domain of a function is the set of all possible input values (often the "x" variable), which produce a valid output from a particular function. The range of a function is the set of possible output values (usually the "y" variable), which result from the function.

For the function 𝑦 = 2𝑥 − 1:

  • The domain is all real numbers because you can substitute any real number for x and get a valid output. So, the domain is (-∞, ∞).

  • The range is also all real numbers because the function can produce any real number for y. This is because the function is a linear function with a non-zero slope (2), which means it will increase without bound as x increases and decrease without bound as x decreases. So, the range is also (-∞, ∞).

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