Verifying inverse functions

Question

Are they inverse functions?

f(x)=3-1/2x

g(x)=-2x+6

yes or no ?

Answer 1

is F(x) = 3 - (1/2)x

or

F(x) = 3 - 1/(2x)

?????

assuming the former....

F(x) = 3 - (1/2)x

F comp G

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3 - (1/2) [ -2x+6] =

3 - [ -x + 3] =

3 +x - 3 = x

G comp F

==========

-2( 3 - (1/2)x) + 6 =

-6 + x + 6 = x

Yes, those two functions are inverses

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Assuming the LATTER, they are NOT inverses...

Regarding F(x) = 3 - 1/ [2x]

0 is not in the domain of F while G is a linear function..

even with domain restrictions, let x = 1/2

3 - 1/ [ 2 * 1/2] = 3 - 1/1 = 3-1 = 2 so (1/2,2) is on F.

But G(2) = (-2)(2)+6 = -4+6 = 2 NOT EQUAL to 1/2.

F maps 1/2 to 2 while G maps 2 to 2.

This is a counterexample that shows they are not inverses..

PLEASE use parenthesis