1 Find fx and gx such that hx f of gx and gx 18x hx 18xto t

1. Find f(x) and g(x) such that h(x) = (f of g)(x) and g(x)= 1-8x

h(x)= (1-8x)(to the power of 3) -5(1-8x)(to the power of 2) +4(1-8x) -1

f(x)=????

2. Graph the function f(x) = x(to the power of 2) -2x-15

Determine on which intervals f(x) is increasing..

a.The function f is increasing on the intervals= ????

Determine on which interval f(x) is decreasing.

b.The function f is decreasing on the intervals=????

Determine the relative maxima or minima.

c.The function has a relative maximum and a maximum value is ????? at x = ?????

d.The function has a relative minimum and the minimum value is ???? at x = ?????

3. A piece of sheet metal is 10 cm by 10 cm. Square corners are cut out so that the sides can be folded up to make a box. Let x represent the length of a cut-out square.

Which function V represents the volume of the box in terms of x?

a. V= x(10-2x)

b. V= 100x

c. V= x(10-2x)(10-2x)

d. V= (10-2x)(to the power of 2)

continued..

What is the domain of the function?

A. x<5

B. 0 < x < 5

C. 0 < x < 20

D. x > 0

continued...

What dimensions approximately yield the maximum volume?

A. 5cm by 5cm by 2.5cm

B. 5cm by 5 cm by 5cm

C. 1.7cm by 1.7cm by 1.7cm

D. 6.6cm by 6.6cm by 1.7cm

4. Given that f(x)= x(to the power of 2) +2, match the function g witha transformation of f.

g(x)= (x+5)(to the power of 2) +2

A. f(x-5)

B. f(5x)

C. f(x+5)

D. f(x) - 5

E. f(x) + 5

F. 5f(x)

5. For f(x) = x - 3/x + 9 , construct and simplify the difference quotient f(x + h) - f(x)/h

f(x+h)-f(x)/h = ????

6. Find (f of g)(x) and (g of f)(x)

f(x)= 25 , g(x)= 0.04

a. (f of g)(x) = ????

b. (g of f)(x)= ????

Solution

1. Given h(x) = (1-8x)^ 3 - 5(1-8x)^2 +4(1-8x) -1

and g(x) = 1-8x

also h(x) = (f of g)(x) = f (g(x)) . It means we replace x with 1-8x in f(x). Now as h(x) = (f of g)(x) = (1-8x)^ 3 - 5(1-8x)^2 +4(1-8x) -1 , hence f(x) must be a cubic function and from this we can say that

f(x) = x^3 -5x^2 +4x -1