a) Let f₁ and f₂ be functions from R to R such that f₁(x) = x² and f₂(x) = x − x². What are the functions f₁ + f₂ and f₁f₂?

Algebra and Trigonometry (6th Edition)
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ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Let  and

1
a) Let f₁ and f₂ be functions from R to R such that f₁(x) x² and f₂(x) = x − x².
What are the functions f₁ + f2 and f₁f₂?
b) Find the domain and range of these functions.
i.
11.
the function that assigns to each pair of positive integers the maximum of
these two integers.
the function that assigns to each positive integer the number of the digits 0,
1, 2, 3, 4, 5, 6, 7, 8, 9 that do not appear as decimal digits of the integer.
c) Find fog, gof where
f(x) = 2x + 1 and g(x) =
3
x-1
, x = 1
d) Letf: Z → Z be such that f (x) = x + 1. Is f invertible, and if it is, what is its
inverse?
e) If f(x) = show that f(a) — f(b) = f(ab).
f) Show that if ad bc # 0, then the function f(x) =
=
ax+b
cx+d
is one-to-one and find its
Transcribed Image Text:1 a) Let f₁ and f₂ be functions from R to R such that f₁(x) x² and f₂(x) = x − x². What are the functions f₁ + f2 and f₁f₂? b) Find the domain and range of these functions. i. 11. the function that assigns to each pair of positive integers the maximum of these two integers. the function that assigns to each positive integer the number of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 that do not appear as decimal digits of the integer. c) Find fog, gof where f(x) = 2x + 1 and g(x) = 3 x-1 , x = 1 d) Letf: Z → Z be such that f (x) = x + 1. Is f invertible, and if it is, what is its inverse? e) If f(x) = show that f(a) — f(b) = f(ab). f) Show that if ad bc # 0, then the function f(x) = = ax+b cx+d is one-to-one and find its
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