Question #0667b

1 Answer
mimi
Dec 12, 2017

#m(x) = –7x#

Explanation:

FUNCTION: equation where every input has exactly one output

Do the Horizontal Line Test (drawing horizontal lines through graph & making sure lines don't cross graph twice) on the original function. If the original function does not pass the Horizontal Line Test, then its inverse will not be a function.
#b(x) = x^2 + 3 -># FAIL
#d(x) = –9 -># FAIL
#m(x) = –7x -># PASS
#p(x) = |x| -># FAIL

Since only one of the functions passed the Horizontal Line Test, there is no reason to test its inverse. It is the only function that could have an inverse function.

SIDE NOTE: Linear functions are always one-to-one & have an inverse function.

Other methods used on inverse to check if it's a function:
- Vertical Line Test on the graphs of each inverse function.
- Testing points
- Input-Output Chart
- Solving for #y#

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