Let f (x) = - 5x+3 and g (x) = 6x-2. Find f •g and it's domain.

f (x) = - 5x+3; g (x) = 6x-2. f. g = (-5x+3) x (6x-2) = â’30x^2 + 10x + 18x â’ 6 = â’30x^2 + 28x â’ 6 Domain is the set of values that the expression is defined or satisfied. = > â’30x^2 + 28x â’ 6 = 0 For the above expression, the domain is real numbers. So x belongs to R.

For this case what you should do is the composition of functions.

f • g = f (g (x)) = - 5 (6x-2) + 3

Rewriting the function we have

f (g (x)) = - 30x + 13

Then, the domain of the function will be that for which the function is defined. In this case, the function is defined for all reals, or equivalently:

x = ( - inf, inf)

answer

f (g (x)) = - 30x + 13

x = ( - inf, inf)