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Zina [86]
3 years ago
12

If g(x) = 3x + 2 and h(x) = 9x2 + 12x + 6, find a function f such that f ○ g = h

Mathematics
1 answer:
Virty [35]3 years ago
6 0
F(g(x)) = f(3x+2) = h(x)=9x^2+12x + 6

Note that (3x+2)^2 = 9x^2 + 12x + 4, which is almost, but not quite, equal to h(x).

Let's experiment.  What if f(x) = x^2 + 2?

Then f(3x+2) = (3x+2)^2 + 2 = 9x^2 + 12x + 4 + 2 = 9x^2 + 12x + 6, which is the same as the given h(x).

Thus, f(x) is x^2 + 2.
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Find the volume of a pyramid with a square base, where the perimeter of the base is 8.2\text{ cm}8.2 cm and the height of the py
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Step-by-step explanation:

The volume of the pyramid is given by:

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We know that the height is:

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Thus we need to find the area of the square at the base.

The perimeter of the square is:

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this means that the length of the sides of the square is :

l=\frac{p}{4}\\ \\l=\frac{8.2cm}{4}\\ \\l=2.05cm

Now we can find the area of the base which the area of the square:

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and finally we find the volume:

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V=\frac{(4.2025cm^2)(13cm)}{3}\\ \\V=\frac{54.6325cm^3}{3}\\ \\V=18.2108cm^3

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