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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?

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mintuchoubay

Answer: Domain of function is [tex] R^{ + } [/tex] or (0, [tex]\infty[/tex] )

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

[tex]x > 0[/tex]

[tex]f(x) > 0[/tex]

Thus, Domain of function is [tex] R^{ + } [/tex] or (0, [tex]\infty[/tex] )

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