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

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

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

replace x values in f(x) with g(x)

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

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

= 18x^2 - 14x -8 -6

= 18x^2 - 14x -14

==> f*g(x) = 18x^2 -14x - 14

==> f*g(-6) = 18(36) +14(6) -14 = 718

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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

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f(x) =2x-6. g(x) =9x^2-7x-4 To find (f*g)(-6).

Solution:

(f*g)(x) =  f(g(x)) = 2g(x)-6

=2(9x^2-7x-4)-6 = 18x^2-14x-8-6 = 18x^2-14x-14.

Therefore,

(f*g)(x) =f(g(x)) = 18x^2-14x-14. Therefore,

(f*g)(-6) = 18(-6)^2-14(-6)-14 = 648 + 84 -14 = 718.