Question

Given f(x) = 4|x-2|+3 and g(x) = 3x²-7, what is f(g(x))?

A) 12x² - 56
B) 12x² - 21
C) 12x² - 15
D) 12x² + 1

Answer 1

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