Consider the function g(x) shown below over a domain of [1,∞). g(x) = 2(x – 1)2 – 3

Part A
Determine g–1(x).

Part B
Identify the domain and range of g(x) and g–1(x). Represent the domains and ranges in inequality, interval, and set notation. Describe the relationship between the domains and ranges of g(x) and g–1(x).

Part C
Graph g(x) and g–1(x). Describe the relationship between the graphs of g(x) and g–1(x).

y=mx+b

step-by-step explanation:

m slope

b y-intercept

x= -3 and

step-by-step explanation:

to find the roots of a cubic, use division or factoring to find the factors then set equal to 0. as this is a difference of cubes, it factors into

where a is the cube root of .

here   this is 27 and the cube root of 27 is 3. so we write using the form:

.

set each factor to 0 and solve for x.

x-3=0

x=3

the quadratic expression does not factor and must be solved using the quadratic formula.

where a = 1, b=3, and c=9

this cubic has two complex roots.