cannot comprehend this for some reason?

Question

f(g(8))

f(x)= 1/x-4
g(x)= 1/x

Answer 1

well this is math question not physics but I'll entertain it anyway:

g(8)=1/8
F(8)=1/(1/8)-4=8-4=4
so f(g(8))=4

Answer 2

I'll concentrate on the basic concept of what's going on, rather than just show you the steps. That may be what's confusing you.

The basic concept you need to understand is what a function is. Working from the top down, f(whatever) means take whatever and put it wherever x appears in the definition of f(x). g(x) means the same thing, but using its definition. The trick is to understand that "whatever" can be anything, including another function. So, f(g(x)) then means take the definition of g(x) (that is, 1/x) and use it to replace the occurrences of x in the definition of f(x). That means f(g(x))= 1/(1/x)-4. Get it? This simplifies to x-4. Now, to find f(g(8)), you just replace that last x with 8. The answer, then is 8-4, or just 4.

Answer 3

f (g (8))

Read this as f of g of eight

It is given that g(x) = 1/x

[g of x] is = g(x) = 1/x

Find g (8) by replacing x by 8.

g (8) = 1/8 = 0.125.

Now [f of g of 8] = f (g (8)).

This can be written as f (X) where X = g (8) or [g of 8]

X = g (8) = 0.125.

Now find [f of X] or f(X) = f (0.125)

It is given that f(x) = (1/x) – 4

Write this as f(y) = (1/ y) in order to avoid confusion. x=y.


Therefore,

f (0.125) = (1/0.12) -4 = 4.

f {g (8)} = 4.