Question

-Let g(x) be a function defined by g(x) = x3.

a) Sketch the graph of g(x).
b) Find the inverse g-1(x) of g(x) then sketch the graph of g-1(x). c) Specify the domain and range of g(x) and g-1(x).
d) Determine the end behavior of g(x) and g-1(x).

Answer 1

Explanation:

a) The graph rises steeply from the third quadrant and there is a point of inflection through the origin (0, 0) then rises steeply in quadrant 1.

b) Let y = g(x) = x^3

x = ∛y

So g(-1)x = ∛x.

The graph is the reflection of g(x) in y = x.

c) Domain of g(x) = All real x, Range is all real g(x).

Domain of g(-1)x = All real x, Range = all real g-1(x).

d) You will see the end behaviour from the graphs.

I tried to send you a link to the graphs but the system wont allow it.