Answer:
The function f be described by
The graph of this function, is the graph of the parent function , which is the parabola with vertex at (0, 0) which opes upwards:
i) reflected with respect to the y-axis, because of the minus
ii) shifted 100 units up
check the picture attached.
A function has an inverse only if it is decreasing or increasing.
So we must divide the following cases for which the inverses exist:
i) with domain (-infinity, 0]
ii) with domain [0, infinity)
To find the formula for the inverse function g of f, we use the property:
f(g(x))=x
thus,
so each of - and + cases, are the inverses of
i) with domain (-infinity, 0]
ii) with domain [0, infinity)
At this point, recall that the domain of a function, is the range of it's inverse function,
and the range of the function, is the domain of the inverse function.
thus,
the range of , which is [0,infinity) is the domain of
i) with domain [0,infinity)
So our answer is:
inverse of i) with domain (-infinity, 0] is
and the inverse of ii) with domain [0, infinity) is
Step-by-step explanation: