Pls help me I’m struggling in this one I tried my best

both the equation listed above and the inverse are functions.

we know that the equation above is a function because firstly, it is a quadratic, which is a type of function. we also know it is a function because there is only 1 output for all of the inputs we can use, or to put it more simply, no matter what x we put in, only one y value comes out.

to find if the inverse is a function, we first have to find the inverse. you can find the inverse to any function by switching the x and f(x) values. after that, solve for the new f(x) value. the result will be the inverse function. the step-by-step process for this one is done below for you.

f(x) = x^2 + 8 > switch the x and f(x)

x = f(x)^2 + 8 > subtract 8 from both sides

x - 8 = f(x)^2 > take the square root of both sides

f(x) =

and this is also a function because we only get one output for every input. therefore, both are functions.