Given 𝑓(𝑥) = 1/2𝑥+1 and g(x) = 3x – 1, determine (f • g)(x) and its domain.

Answer 1

f(x) = (1/2)x +1

g(x) = 3x-1

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

the domain of x is any real number

UNLESS you

meant f(x) = 1/(2x) +1

then

f(g(x)) = 1/(2(3x-1) +1 = 1/(6x-2) + 1 = (1+6x-2)/(6x-2) = (6x-1)/(6x-2)

an the domain of x is any real number except x=1/3. as it makes the denominator =0 and the expression undefined

you've written the latter way, so it would likely be the correct answer

but people on line often intend it the 1st way, so it's almost a toss up which way to go