Let f(x)=2x^2+x-3 and g(x)=x-1. perform the indicated operation, then find the domain. (f*g)(x) answers: a. 2x^3-x^2-4x+3; domain: all real numbers b. 2x^3+x^2-3x; domain: all real numbers c. 2x^3+x^2+4x-3; domain: negative real numbers d. 2x^2+x-3x+3; domain: positive real numbers i'd appreciate any i can get! i don't want just the answer, i'd like to know the steps too so i can figure out how to do this in the future!

asnwer is (g o h o f)(x) = 2x - 6/x + 7

step-by-step explanation:

given,

f(x) = x - 3/x

g(x) = x + 3

h(x) = 2x + 1

we need to find : (g o h o f)(x)

we can write (g o h o f)(x) = g[ h{ f(x) } ]

so first we find h{f(x)}

h{f(x)} = f(x) + 3 = (x - 3/x) + 3

h{f(x)} = x - 3/x + 3

now we find g[ h{ f(x) } ].

g[ h{ f(x) } ] = g(x - 3/x + 3)       {plug h{f(x)} = x - 3/x + 3 in g[h{f(x)}] }

g(x - 3/x + 3) = 2 (x - 3/x + 3) + 1

                    = 2x - 6/x + 6 + 1

                    = 2x - 6/x + 7

hence we get (g o h o f)(x) = 2x - 6/x + 7