how can i graph each function and determine whether the inverse of each function is also a function?

Question

like this problems

f(x) = Xsquare + x

g(x)= Xcube + 1

Answer 1

You graph the fuctions by picking a few values of x, both positive and negative. The inverse function will have the axes reversed: the y-axis becomes the x-axis of the inverse function. Then there should be only one value for y for each x. Therefore, if the function has values on both sides of the y-axis for any portion of its range, the inverse is not a function.

Answer 2

An inverse relation takes a relation y=f(x), and swaps x and y. If the unique relation is y=3x+a million, then the inverse relation is x=3y+a million. you are able to rewrite this (and graph it) as y=(x-a million)/3. using fact the inverse is defined everywhere, would be written explicitly in terms of x, and with out the +/- that comes once you're taking the sq. root of the two factors, it must be a function. often, the inverse -- of a real-valued, continuous function of the genuine numbers -- is a function on each and every occasion the unique function is precisely monotonic, it particularly is, continuously-increasing or continuously-lowering. this is the case with non-consistent linear purposes which comprise f(x)=3x+a million

Answer 3

you use the pencil/vertical line test. Or you look to see if they are reflections across the y=x line.