Final answer:
To find f(g(x)), substitute g(x) into the expression for f(x) and simplify.
Step-by-step explanation:
To find f(g(x)), we need to substitute g(x) into the expression for f(x). Given f(x) = 4|x-2|+3 and g(x) = 3x²-7, we have:
f(g(x)) = 4|g(x)-2|+3
= 4|3x²-7-2|+3
= 4|3x²-9|+3
Since |3x²-9| is always positive, we can remove the absolute value signs and simplify the expression:
= 4(3x²-9)+3
= 12x² - 36 + 3
= 12x² - 33