Determine the domain and range of:
y = 5 – [1/ (1 + x)]
So, would the domain be all real numbers except -1? And would the range be all real numbers except zero? I'm really confused. . .
Domain is correct. Range is all real numbers except 5. Since 1/(1+x) can never be 0, the equation will never be 5. Write back if you still have questions.
ok thank you!
To determine the domain and range of the given function y = 5 - [1/(1 + x)], let's start by analyzing the restrictions on the independent variable (x).
Domain:
The domain of a function represents all the possible inputs (x-values) for which the function is defined. In this case, we need to identify any potential values of x that would make the denominator (1 + x) equal to zero, as division by zero is undefined.
Since we cannot divide by zero, we set the denominator equal to zero and solve for x:
1 + x = 0
x = -1
Therefore, x = -1 is not in the domain of the function. Consequently, the domain of the function y = 5 - [1/(1 + x)] is all real numbers except -1.
Range:
The range of a function represents all the possible outputs (y-values) that the function can produce corresponding to the given inputs (x-values). To determine the range, we need to examine the behavior of the function as x approaches positive or negative infinity.
As x approaches positive or negative infinity, the term 1/(1 + x) becomes infinitely close to zero, which means it tends towards the limit of 0. Therefore, the range of the function includes all real numbers except zero.
So, the domain of the function y = 5 - [1/(1 + x)] is all real numbers except x = -1, and the range is all real numbers except y = 0.