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777dan777 [17]
3 years ago
6

Define a function f on a set of real numbers as follows: f(x) = 3x − 1 x , for each real number x ≠ 0 Prove that f is one-to-one

. Proof: Let x1 and x2 be any nonzero real numbers such that f(x1) = f(x2). Use the definition of f to rewrite the left-hand side of this equation. (Enter the answer as an expression in x1.) Then use the definition of f to rewrite the right-hand side of f(x1) = f(x2). (Enter the answer as an expression in x2.) Equate the expressions obtained for the left- and right-hand sides of f(x1) = f(x2), and simplify the result completely. The result is the following equation. x1 = Therefore, f is .
Mathematics
1 answer:
dalvyx [7]3 years ago
6 0

Answer with Step-by-step explanation:

We are given that

f(x)=\frac{3x-1}{x}

For each real number x\neq 0

To prove that f is one -to-one.

Proof:Let x_1 and x_2 be any nonzero real numbers such that

f(x_1)=f(x_2)

By using the definition of f to rewrite the left hand side of this equation

f(x_1)=\frac{3x_1-1}{x_1}

Then, by using the definition of f to rewrite the right hand side of this equation  of f(x_1)=f(x_2)

f(x_2)=\frac{3x_2-1}{x_2}

Equating the expression then we get

\frac{3x_1-1}{x_1}=\frac{3x_2-1}{x_2}

3x_1x_2-x_2=3x_2x_1-x_1

3x_1x_2-3x_1x_2+x_1=x_2

x_1=x_2

Therefore, f is one-to-one.

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