Evaluate (f compositefunction h)(-21) assuming that f(x) = squareroot x + 1 and

Question

Evaluate (f compositefunction h)(-21) assuming that f(x) = squareroot x + 1 and h(x) = |x + 2|. Evaluate (g compositefunction h)(-8) assuming that g(x) = x/x + 1 and h(x) = |x + 2|. A) 6/7 B) -6/7 C) 7/6 D) -7/6 Suppose h(x) = 6 + squareroot 6/x^2 + 36. If g(x) = 6/x^2 + 36, then find a function f such that h = f compositefunction g. A) f(x) = 6 - x B) f(x) = squareroot x - 6 C) f(x) = 6 - x^2 D) f(x) = 6 + squareroot x Suppose f(x) = 20x + 1. Find a formula for f^-1. Suppose f(x) = -x - 11. Evaluate f^-1 (-6). A) -5 B) 9 C) 10 D) 11 Suppose f(x) = 1/13x - 27. Find the domain of f.

Explanation / Answer

1. f(x) = sqrt(x+1) , h(x) = | x+2|

(foh)(-21) =f(h(-21))

And h(-21) = | -21 +2 | =| -19 | =19

Therefore f(h(-21)) =f(19) =sqrt(19+1) = sqrt20=2sqrt5

2. g(x) = x/(x+1) , h(x) = | x + 2 |

(goh)(-8) = g(h(-8))

And h(-8) = | -8 +2 | =6

Therefore g(h(-8)) =g(6) =6/(6+1) =6/7

c . h(x) = 6 +sqrt(6/x^2 +36) , g(x) = 6/x^2 +36

We replace 6/x^2 +36 by g(x)

So we get

h(x)= 6+sqrt g(x)

And h=fog

Therefore f(x) =6+sqrt x

4. y=f(x) =20x +1

Switching x and y

x=20y+1

20 y =x-1

y=(x-1)/20

f-1(x) =(x-1)/20

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