If f(x) = -3x + 7 and g(x) = x^2 +7x-2, find (fog)(-2)?

PROBLEM 1:

(f o g)(x) --> means f of g of x

Or written another way, you are looking for:

f(g(x))

You want to work from the inside out.

So first compute g(x) with -2:

g(x) = x² + 7x - 2

g(-2) = (-2)² + 7(-2) - 2

g(-2) = 4 - 14 - 2

g(-2) = -12

Now plug that result (-12) into f(x):

f(x) = -3x + 7

f(-12) = -3(-12) + 7

f(-12) = 36 + 7

f(-12) = 43

Answer:

(fog)(-2) = 43

PROBLEM 2:

After a 14% reduction, a tracksuit sold for $38.

Let x be the original price.

After a 14% reduction we have 86% of the original price being $38.

Write an equation:

0.86x = 38

Divide both sides by 0.86:

x = 38/0.86

x = 44.18604651...

Round to the nearest whole cent.

Answer:

$44.19

g(-2) = (-2)² + 7(-2) - 2

g(-2) = 4 - 14 - 2

g(-2) = -12

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f(g(-2)) ---> f(-12) since g(-2)'s value was found as -12, --->

f(-12) = -3(-12) + 7

f(-12) = 36 + 7

f(-12) = 43

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I did the problem myself (as you can see) but here's a Calculator for verification:

https://www.symbolab.com/solver/function-compositi...

Thomas made a small calculation error,

his method (which you can also do, plugging in every x with g(x) THEN plugging in (-2) would come up with

-3(-2)² - 21(-2) + 6 + 7 ---> - 12 + 42 + 13 ---> - 12 + 55

= 43

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Problem #2:

x - 0.14x = 38

0.86x = 38

x = 38/0.86

x = 44.18604651162791

≈ $ 44.00

(fog)(x)=-3(x^2+7x-2)+7

(fog)(x)=-3x^2-21x+6+7

(fog)(x)=-3x^2-21x+12

(fog)(-2)=42