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
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.
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