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dezoksy [38]
3 years ago
7

If f(x) = 3x^2 -2x-1 and g(x) = x^2 find (gof) (x)

Mathematics
1 answer:
emmainna [20.7K]3 years ago
3 0

Answer:

A

Step-by-step explanation:

Substitute x = f(x) into g(x), that is

g(f(x))

= g(3x² - 2x - 1)

= (3x² - 2x - 1)² = (3x² - 2x - 1)(3x² - 2x - 1)

Each term in the second factor is multiplied by each term in the first factor, that is

3x²(3x² - 2x - 1) - 2x(3x² - 2x - 1) - 1(3x² - 2x - 1) ← distribute parenthesis

= 9x^{4} - 6x³ - 3x² - 6x³ + 4x² + 2x - 3x² + 2x + 1 ← collect like terms

= 9x^{4} - 12x³ - 2x² + 4x + 1 → A

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Step-by-step explanation:

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Evaluate : <br> \(\cos 12 \cos 24 \cos 36 \cos 48 \cos 72 \cos 84\)
NeTakaya
The answer in itself is 1/128 and here is the procedure to prove it:
cos(A)*cos(60+A)*cos(60-A) = cos(A)*(cos²60 - sin²A) 

<span>= cos(A)*{(1/4) - 1 + cos²A} = cos(A)*(cos²A - 3/4) </span>

<span>= (1/4){4cos^3(A) - 3cos(A)} = (1/4)*cos(3A) </span>

Now we group applying what we see above

<span>cos(12)*cos(48)*cos(72) = </span>
<span>=cos(12)*cos(60-12)*cos(60+12) = (1/4)cos(36) </span>

<span>Similarly, cos(24)*cos(36)*cos(84) = (1/4)cos(72) </span>

<span>Now the given expression is: </span>

<span>= (1/4)cos(36)*(1/4)*cos(72)*cos(60) = </span>

<span>= (1/16)*(1/2)*{(√5 + 1)/4}*{(√5 - 1)/4} [cos(60) = 1/2; </span>
<span>cos(36) = (√5 + 1)/4 and cos(72) = cos(90-18) = </span>
<span>= sin(18) = (√5 - 1)/4] </span>
<span>And we seimplify it and it goes: (1/512)*(5-1) = 1/128</span>
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I think it’s 3 but I’m not sure

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What is the value of x in the equation 2(x-3)+9=3(x+1)+x?<br> O x=-3<br> x X=-1<br> x = 0<br> x=3
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Answer:900000

Step-by-step explanation:

Use a calculator

5 0
3 years ago
Read 2 more answers
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