Evaluate the function

Question

Refer to function f,g, and h. Evaluate the function for the given value of x. Write any number in the answer as an integer or a simplified fraction.

f(x)=x^3-3x g(x)=square roof of 3x h(x)=8x-1

f(g(12))is _____

Answer 1

g(12) = sqrt(3*12) = sqrt(36) = 6

then

f(6) = 6^3 - 3*6 = 216-18 = 198

now the hard way to do it:

f(g(x)) = [sqrt(3x)]^3 - 3 * sqrt(3x)

= (3x) * sqrt(3x) - 3 * sqrt(3x)

= 3*sqrt(3x) [ x - 1]

f(g(12)) = 3 * sqrt(3*12) * [12-1]

= 3 * sqrt(36) * 11

= 3*6*11

= 18*11

= 18*(10 + 1)

= 18*10 + 18*1

= 180 + 18

= 198