Question

The domain of the given function is a set of all positive real numbers. Find its range. F(x) =3x-1

Answer 1

The domain of f(x)=3x−1 is, then, the entire set of Real Numbers, R, since there doesn't exist any value of x on the entire number line such that 3x−1 will be undefined.

Answer 2

Here's the answer you are looking for

f(x) = 3x - 1

Let f(x) = y

So
⏩y = 3x - 1

We need to find the range.

y = 3x - 1

3x = y + 1

$x = \frac{y + 1}{3}$

The domain for this function is equal to the range of the function, y = 3x - 1

So, in this function, there is no variable in the denominator nor any root overs, so there is no restrictions in the value of y.

But x can take only positive values that is greater than 0.

So, y > 3(0) - 1

y > -1

⏩ Therefore, the range of the function f(x) = 3x - 1 is a set containing all numbers greater than -1.

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