Determine the implied domain of the given function. Express in interval notation
(-4x^(2)-3x)/(2)
Why can't x be any real or complex number?
THat's what the assignment says. I don't understand it
The domain of x goes from -infinity to + infinity.
f(x) = - (4x^2+3x)/2 =(-1/2)x(4x+3)
sketch a graph
x f(x)
-oo -oo
-3 -13.5
-2 -5
-1 -1/2
-3/4 0
-1/2 +.25
0 0
+1 -7/2
+oo -oo
it's domain is fine for all real x
On the other hand the range is limited and never gets higher than 9/32 at x = -3/8
To determine the implied domain of a function, we need to find the values of x for which the function is defined. In this case, the given function is
f(x) = (-4x^2 - 3x)/2
The only potential concern when it comes to defining a function is dividing by zero. Therefore, we need to find the values of x for which the denominator is not equal to zero.
In this case, the denominator is 2, which is a constant and is never equal to zero. So, we don't have any restrictions on the domain due to division by zero.
Hence, the implied domain of the given function is all real numbers.
Expressed in interval notation, the implied domain is (-∞, +∞).