Question

20 POINTS please explain well

Answer 1

The difference of course is the symbol between the f and g letters.

The circle $\circ$ notation means we're doing a function composition.

Writing $(f \circ g)(x)$ is the same as saying $f(g(x))$ where g is the inner function.

Here's an example

f(x) = x^2

g(x) = 3x

f( g(x) ) = ( g(x) )^2 ... note how x is replaced with g(x)

f( g(x) ) = ( 3x )^2

f( g(x) ) = 9x^2

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On the other hand, the dot notation means we multiply the f(x) and g(x) functions.

Going back to the previous example, we could say

$f(x) = x^2\\\\g(x) = 3x\\\\(f \cdot g)(x) = f(x)*g(x)\\\\(f \cdot g)(x) = x^2*3x\\\\(f \cdot g)(x) = 3x^3$