Respuesta :
v(x) = (2x - 3)/(5x + 4) The domain is all Real numbers except x = -4/5, because if x = -4/5 the denominator would be zero and you cannot divide by zero.{x | x ∈ R, x ≠ -4/5} w(x) = (5x + 4)/(2x - 3)similarly, x ≠ 3/2so, {x| x ∈ R, x ≠ 3/2}
The domain of s(x) over t(x) is all real numbers except at x=-4/5. The domain of w(x) is all real numbers except at x=-3/2.
What is the domain and range of a function?
- The domain is the set of values for which the given function is defined.
- The range is the set of all values which the given function can output.
The domain of a function is the value of the independent variable, generally, x for which the given function is defined.
For a function that is made up of the fraction of two polynomials, the function is not defined when the value of the denominator becomes zero.
The domain of s(x) over t(x) will be all real numbers, except the number that makes the denominator equal to zero, therefore, t(x) should not be zero.
t(x) = 0
5x + 4 = 0
5x = -4
x = -4/5
Hence, the domain of s(x) over t(x) is all real numbers except at x=-4/5.
Similarly, The domain of w(x) will be all real numbers, except the number that makes the denominator equal to zero, therefore, s(x) should not be zero.
s(x) = 0
2x - 3 = 0
2x = 3
x = 3/2
Hence, the domain of w(x) is all real numbers except at x=-3/2.
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