Question

The length of a rectangle is 5 in. More than 3 times its width. The quadratic function f(x) = x(3x + 5) represents the area of the rectangle in terms of its width. What is a reasonable domain of the function?

Answer 1

Answer: Domain of function is $R^{ + }$ or (0, $\infty$ )

Step-by-step explanation:

Assuming x as width of rectangle

so, Width = x

Question says, Length is 5in more than 3 times id width.

we write as Length = 3x+5

Therefore, Area of rectangle will be given function f(x)

f(x) = x(3x+5)

Here, It is important to notice that width and length of rectangle will always be positive values and also, area of rectangle is always positive.

we can write in equation as

$x > 0$

$f(x) > 0$

Thus, Domain of function is $R^{ + }$ or (0, $\infty$ )