Algebra Answers

3. The function f is defined by f(x) = ax + b for x € R, where a and b are constants. It

is given that f(2) = 1 and f(5) = 7.

i) Set up a pair of simultaneous equations using the information given.

ii) Solve them and find the values of a and b.

iii) Solve the equation f(f(x)) = 0.

you are to report what you have research and present exponential or logarithmic functions

Prove by mathematical induction that n^2+n < 2^n whenever n is an integer greater

than 4.

Of 350 students polled, some have a cat, some have a dog, and some have both. One hundred seventy-five students have a cat and 140 have both types of pets. How many students have a dog only? Explain

The marketing research department for a company that manufactures and sells notebook computers established the following price-demand and revenue functions for the company

R(x)= x(1190-360x)

C(x)= 4320+146x

Both have domain 1≤x≤20.

a)Form a profit function P and graph R, C, and in the same rectangular coordinate system using 3-unit intervals.

b)Discuss the relationship between the intersection points of the graph R and C and the q intercept of P

c)Determine the break-even point graphically.

Solve the following quadratic programming problem(Wolf’s method)

Maximize         Z = 2x₁+x₂-x₁²,

Subject to        2x₁+3x₂ ≤ 6,

                          2x₁+x₂ ≤ 4,

               x₁, x₂≥ 0

b) f(x) = −3x2 + 7

c) f(x) = (x + 1)∕(x + 2)

assuming you are a researcher tasked to know about some truths in life. you plan to investigate the growth or decay of some things that interest you. you are to report what you have researched and present exponential or logarithmic functions that would model the involved quantities. you also have to present the graph and explain its characteristics or behavior.

Find a number that provides a counterexample to show that the given statement is false: For

all numbers x, |x + 3| = |x| + 3