given f(x)=2x-6 and g(x)=9x^2-7x-4. Find (f*g)(-6).

In order to find the value of the composition of 2
functions, in our case f and g, we have to follow the
steps:

Step 1: First, we have to find out the expression of
the composition of the 2 functions:

(f*g)(x) =
f(g(x))

To find f(g(x)) we have to substitute x by g(x) in
the expression of f(x):

f(g(x)) =
2*(g(x))-6

Now, we'll substitute g(x) by it's
expression:

2*g(x)-6 = 2*(9x^2-7x-4) -
6

We'll open the
brackets:

2*(9x^2-7x-4) - 6 = 2*9x^2 - 2*7x - 2*4 -
6

f(g(x)) = 18x^2 - 14x  -
14

Step 2:

Now, we'll
calculate the value (f*g)(-6), substituting x from the expression of (f*g)(x), by
(-6).

(f*g)(-6) = 18(-6)^2 - 14(-6)  -
14

(f*g)(-6) = 648 + 84 -
14

(f*g)(-6) =
718