Define a function f on a set of real numbers as follows. ffx)= 3X - 1. for each real number x 0 Is fis one-to-one? To answer this question, let x, and x, be any nonzero real numbers such that f(x,) = f(x,). Use the definition of f to rewrite the left-hand side of this equation. (Enter the answer as an expression in x,) Then use the definition of f to rewrite the right-hand side of f(x,) = f(x). (Enter the answer as an expression in x.) Equate the expressions obtained for the left- and right-hand sides of f(x,) = f(x,), and simplify the result completely. The result is the following equation. x = Therefore, f is one-to-one Need Help? Read It
Define a function f on a set of real numbers as follows. ffx)= 3X - 1. for each real number x 0 Is fis one-to-one? To answer this question, let x, and x, be any nonzero real numbers such that f(x,) = f(x,). Use the definition of f to rewrite the left-hand side of this equation. (Enter the answer as an expression in x,) Then use the definition of f to rewrite the right-hand side of f(x,) = f(x). (Enter the answer as an expression in x.) Equate the expressions obtained for the left- and right-hand sides of f(x,) = f(x,), and simplify the result completely. The result is the following equation. x = Therefore, f is one-to-one Need Help? Read It
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Define a function f on a set of real numbers as follows.
3x - :
f(x) =
E, for each real number x + 0
Is f is one-to-one?
To answer this question, let x, and x, be any nonzero real numbers such that f(x,) = f(x). Use the definition of f to rewrite the left-hand side of this equation. (Enter the answer as an expression in x,.)
Then use the definition of f to rewrite the right-hand side of f(x,) = f(x,). (Enter the answer as an expression in x..)
Equate the expressions obtained for the left- and right-hand sides
f(x,) = f(x,), and simplify the result completely. The result is the following equation.
X, =
Therefore, f is one-to-one
Need Help?
Read It
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