Urgent Math help!!!?

Question

I have a New York state Math B exam tommorrow, and i need to know the concept of this idea. Please provide an answer and detailed steps on how to achieve it!
Thanks in advance
f(x)=x^2/3 and g(x)=8x^-1/2, find (f o g)(x) and find (f o g)(27)

Answer 1

Hi...I can help. Ok...

(f o g) (x) means (8x^-1/2) ^2/3.

What happens there is that u take the entire function g(x) and insert it wherever 'x' occurs in the function f(x). In the same way if the question were ' find (g o f) (x), you would take the entire f(x) and insert it where ever 'x' occurs in g(x). So ( g o f) (x) would be 8(x^2/3)^-1/2. (f o g) (27) would be (8(27) ^-1/2)^2/3. What was done there is that u insert 27 where 'x' occurs in the function (f o g)(x).

Hope this helps....good luck

Answer 2

it is like saying: (f o g)(x) = f(g(x)).
f(g(x)) = (8x^-1/2)^2/3 = (8^2/3)x^-1/3
for the last part, f(g(27))

Answer 3

(fog)(x)=f[g(x)]=f(8x^-1/2)=(8x^-1/2)^2/3=8^2/3*x^-1/3

(fog)(27)=8^2/3*27^-1/3