Exploring the Range of Functions: Solving for Inverse and Restrictions

[mathdad]

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?

 

[skeeter]

$y = \dfrac{1}{x}$ is a basic parent function whose graph is easily sketched ... so, sketch it and answer your own question.

 

[mathdad]

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?

 

[skeeter]

you asked the same question in your other post ...

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