What is the range of f(x) = 1-3x   if the domain is x>0?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The domain of a function is all the values of x for which f(x) yields real values.

The values of f(x) when x lies in the domain is the range.

Here x > 0 and f(x) = 1 - 3x

The range is all numbers less than 1.

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll have to determine the set of real numbers that variable x can take, such as the expression that defines the function to be real.

We'll set f(x) = y = 1 - 3x

We'll move the term in x to the left and the term in y to the right:

3x = 1 - y

We'll divide by 3:

x = (1-y)/3

We know, from enunciation, that x>0, therefore (1-y)/3 > 0.

We'll solve the inequality:

(1-y)/3 > 0

1 - y > 0

-y > -1

We'll multiply by -1 and we'll change the direction of inequality:

y < 1

Therefore, the range of the function f is the opened interval (-`oo` ; 1).

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