Exploring the Range of Functions: Solving for Inverse and Restrictions

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In summary, the range of the function y = 1/x is all real numbers except for 0. This can be represented on the graph by a curve that does not cross the lines x = 0 and y = 0, with a domain of all real numbers except for 0. This is also known as the inverse function of x = 1/y, with a domain of all real numbers except for 0.
  • #1
mathdad
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Find the range algebraically.

y = 1/x

Find inverse of y.

x = 1/y

Solve for y.

yx = (1/y)(y)

yx = 1

y = 1/x

f^(-1) x = 1/x

The domain of f^(-1) x is ALL REAL NUMBERS except that x cannot be 0.

So, the range of y = 1/x is ALL REAL NUMBERS except that y cannot be 0.

Correct?
 
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  • #2
$y = \dfrac{1}{x}$ is a basic parent function whose graph is easily sketched ... so, sketch it and answer your own question.
 
  • #3
I know what this graph looks like. I've seen it hundreds of times but what does it mean to a novice math learner? There is a curve in quadrants 1 and 3 that does not cross the lines x = 0 and y = 0. The textbook answer is (-infinity, 0) U (0, infinity). What on the graph tells me that this is the correct range?
 
  • #4
you asked the same question in your other post ...

http://mathhelpboards.com/pre-calculus-21/range-functions-4-a-21775.html#post98495
 

Related to Exploring the Range of Functions: Solving for Inverse and Restrictions

1. What is a range of functions?

A range of functions refers to the set of all possible output values that can be produced by a function for a given set of input values.

2. How is the range of a function determined?

The range of a function is determined by examining the set of all possible output values that can be produced by the function for a given set of input values.

3. Can a function have an infinite range?

Yes, a function can have an infinite range if it has an unbounded domain, meaning there is no limit to the possible input values.

4. What is the difference between domain and range?

The domain of a function refers to the set of all possible input values, while the range refers to the set of all possible output values.

5. How can the range of a function be visualized?

The range of a function can be visualized by plotting the input and output values on a graph, where the output values are represented on the y-axis and the input values on the x-axis.

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