What is the least value of a such that the function;
g: [a, ∞) -> R, g(t) = (3t) / (5+t^2) has an inverse function?
This clearly means that a horizontal line will cut the graph at most twice unless we restrict the domain to one of the three regions. Clearly satisfies the given constraint.
To find the inverse of a function first you should check the interval where the function is bijective.for your question its bijective at
since for your question is [a,+inf] so by using 2) a must be equal to 5^1/2
I am attacing a rough image.
Hope this helps.