Which equation is the inverse of y = 100 – x2? mc010-1.jpg mc010-2.jpg mc010-3.jpg mc010-4.jpg

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 

Agc and bgd are vertical angles