Final answer:
The function Y = √ X+4 for X ≥ -4 does have an inverse that is a function. This is determined by using the Horizontal Line Test which shows that no horizontal line can intersect the function at more than one point, implying that the function's inverse is also a function.
Step-by-step explanation:
The function given is Y = √ X+4, for X ≥ -4. This is a square root function and it is a continuous function on its domain [-4, +∞).
To investigate if this function has an inverse that is also a function, we can apply the Horizontal Line Test. If any horizontal line can intersect with the function at more than one point, then the function does not have an inverse that is a function. However, in this case, no horizontal line can intersect the square root function at more than one point, implying that its inverse would also be a function.
Learn more about Inverse of a Function