math homework need to be done in 5 hours max

Name:

Week 2 Homework (Algebra Review) Due 7/5/2019 at 9 am

1) Let f(x) = x2 + 4x and g(x) = 3x− 5. Find the the following compositions

(a) f ◦g(x)

(b) g ◦f(x)

2) Find the domain and range of the following functions

(a) f(x) = √

9 −x2.

(b) f(x) = 4 −x2.

(c) f(x) = 5 + √

9 −x.

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3) Solve the following equations and inequalities

(a) e4x − 7 = 6e2x (Hint: Make a substitution!).

(b) x2 − 2x ≥ 3

(c) sin (2x) + cos2 (2x) = 1 where 0 ≤ x ≤ 2π.

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(d) 3

x −x− 2 < 0.

4) Let f(x) = x2 − 3x− 5. Find and simplify

f(x + h) −f(x) h

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5) Let f(x) = x2 + 5x. Find and simplify

f(x) −f(t) x− t

6) Simplify the following expressions as much as possible

(a) x− 9 √ x− 3

(b) (x + h)2 −x2

h

4

7) Factor the following polynomials. (Try to do it first without any online help, otherwise it doesn’t make sense.)

(a) x2 + 7x− 8

(b) 4x2 + 12x + 5

(c) 18x3 + 3x2 − 6x

8) Why is the following statement false?

(x− 1) (x + 1)(x− 1)

= 1

x + 1 .

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