What is the range of the equation

The range of the equation is

Explanation:

The given equation is

We need to determine the range of the equation.

Range:

The range of the function is the set of all dependent y - values for which the function is well defined.

Let us simplify the equation.

Thus, we have;

This can be written as

Now, we shall determine the range.

Let us interchange the variables x and y.

Thus, we have;

Solving for y, we get;

Applying the log rule, if f(x) = g(x) then , then, we get;

Simplifying, we get;

Dividing both sides by , we have;

Subtracting 7 from both sides of the equation, we have;

Dividing both sides by 2, we get;

Let us find the positive values for logs.

Thus, we have,;

The function domain is

By combining the intervals, the range becomes

Hence, the range of the equation is

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )

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