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1) f(p) = 4 / p ; g(p) = (p - 2) / 3

(f o p) = 4 / (p - 2) / 3 = 4x3 / (p - 2) = 12 / p - 2

2.

) I(u) = (1000 - 2U).

U = 1000U - 2U²

I(100) = 1000(100) - 2(100²) = 100000 - 20000 = 80000

3.

)

<img src="https://tex.z-dn.net/?f=f%28n%29%3D50%2B%20%5Csqrt%7B%20%5Cfrac%7Bn%7D%7B150%7D%7D%20" /> g(x) = 4x + 3

f(g(x)) = <img src="https://tex.z-dn.net/?f=50%2B%20%5Csqrt%7B%20%5Cfrac%7B4x%2B3%7D%7B150%7D%7D%20" />

4.

) G(t) = 40 - 2t :

G - 40 = - 2t - G / 2 - (40 / - 2) = t

20 - (G / 2) = t

5.

)

<img src="https://tex.z-dn.net/?f=f%28x%29%3D2%20%5Csqrt%7BX-1%7D%20" />

<img src="https://tex.z-dn.net/?f=g%28X%29%3D%20%5Cfrac%7B2%7D%7BX%2B2%7D%20" />

(f + g)(2)

<img src="https://tex.z-dn.net/?f=2%5Csqrt%7BX-1%7D%2B%20%5Cfrac%7B2%7D%7BX%2B2%7D%3D%20%5Cfrac%7B%28X%2B2%29%282%5Csqrt%7BX-1%7D%29%2B2%7D%7BX%2B2%7D%20%20%20" />

<img src="https://tex.z-dn.net/?f=%28X%2B2%29%282%20%5Csqrt%7BX-1%7D%29%3D2X%5Csqrt%7BX-1%7D%2B4%5Csqrt%7BX-1%7D%20" />

<img src="https://tex.z-dn.net/?f=%28f%2Bg%29%28x%29%3D%20%5Cfrac%7B2X%5Csqrt%7BX-1%7D%2B4%5Csqrt%7BX-1%7D%2B2%7D%7BX%2B2%7D%20" />

<img src="https://tex.z-dn.net/?f=%28f%2Bg%29%282%29%3D%20%5Cfrac%7B2%282%29%5Csqrt%7B2-1%7D%2B4%5Csqrt%7B2-1%7D%2B2%7D%7B2%2B2%7D%20" />

(f + g)(2) = \ frac{4 \ sqrt{1} + 4 \ sqrt{1} + 2}{4}

<img src="https://tex.z-dn.net/?f=%28f%2Bg%29%282%29%3D%20%5Cfrac%7B4%2B4%2B2%7D%7B4%7D" />

(f + g)(2) = 10 / 4 = 5 / 2

6.

)

<img src="https://tex.z-dn.net/?f=f%28x%29%3D%20%5Cfrac%7B5000X%7D%7BX%2B100%7D%20" />

Y(X + 100) = [5000X / (X + 100)](X + 100)

Y(X + 100) = 5000X

Y(X) + Y(100) = 5000X

5000X = YX + 100Y

5000X - YX = 100Y - X(Y - 5000) = 100Y

X = 100Y / - (Y - 5000)

X = - 100Y / (Y - 5000)

X = Y

Y = - 100X / (Y - 5000)

[img = 10].