Question

AYUDA CON FUNCIONES ahora urgente

Answer 1

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.) 
$f(n)=50+ \sqrt{ \frac{n}{150}}$  g(x) = 4x + 3

f(g(x)) = $50+ \sqrt{ \frac{4x+3}{150}}$

4.) G(t) = 40 - 2t:

G - 40 = -2t

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

20 - (G/2) = t

5.)
 
$f(x)=2 \sqrt{X-1}$

$g(X)= \frac{2}{X+2}$

(f+g)(2)

$2\sqrt{X-1}+ \frac{2}{X+2}= \frac{(X+2)(2\sqrt{X-1})+2}{X+2}$

$(X+2)(2 \sqrt{X-1})=2X\sqrt{X-1}+4\sqrt{X-1}$

$(f+g)(x)= \frac{2X\sqrt{X-1}+4\sqrt{X-1}+2}{X+2}$

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

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

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

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

6.)
$f(x)= \frac{5000X}{X+100}$

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)

$f^{-1}(X) = \frac{-100X}{(Y - 5000)}$