Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = the quantity x minus seven divided by the quantity x plus three. and g(x) = quantity negative three x minus seven divided by quantity x minus one.

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = the quantity x minus seven divided by the quantity x plus three. and g(x) = quantity negative three x minus seven divided by quantity x minus one.

Mathematics
See more answers at brainly.com
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

\[f(x)=\frac{ x-7 }{ x+3 } g(x)=\frac{ -3x-7 }{ x-1 }\]
prepare to do a raft of algebra
ah okay thank you for your help in advance btw :)

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

\[f(x)=\frac{ x-7 }{ x+3 } \] and \[g(x)=\frac{ -3x-7 }{ x-1 }\] right?
yes
this is amazingly easy for me to write the composition one way by using copy and paste i am going to past \(g(x)=\frac{ -3x-7 }{ x-1 }\)where every i see an \(x\) in \(f(x)=\frac{ x-7 }{ x+3 }\)
\[f(x)=\frac{ x-7 }{ x+3 }\] \[f(g(x))=\frac{ \frac{ -3x-7 }{ x-1 }-7 }{ \frac{ -3x-7 }{ x-1 }+3 }\]
okay i did that and now do i just solve?
now comes the raft of algebra part
which will end up with an orgy of cancellation since your answer should be \(x\)
it is not really that bad multiply top and bottom of that complex fraction by \(x-1\) to clear the denominator don't forget the distributive law
okay let me just do it real quick
would i do the same for the g(f(x)) = x. later on?
yes, just clear the denominators then all will go bye bye
ah thank you so much!
yw
wait im so lost what happens with the -7 and 3?
don't forget the distributive law !!
????
\[\frac{ \frac{ -3x-7 }{ x-1 }-7 }{ \frac{ -3x-7 }{ x-1 }+3 }\times \frac{x-1}{x-1}\] \[=\frac{-3x-7(x-1)}{-3x-7+3(x-1)}\] is a start
the distributive law in action denominators go, but you still have to distribute now distribute again, the -7 up top and the 3 below then combine like terms
okay at the denominator should i add the 7 and 3 before distrubuting or no?
distribute first
numerator should be \(-10x+7\) if you do it correctly
okay just a min
the denom i got -10
yeah that is right, and i lied, the numerator is \(-3x-7-7(x-1)=-3x-7-7x+7=-10x\)
and of course \(\frac{-10x}{-10}=x\) as needed
ah okay thats easy in reality thanks! ill do the other side now
good luck it is real similar
i just am stuck a little after muliplying x+3/x+3
\[g(x)=\frac{ -3x-7 }{ x-1 }\] \[g(f(x))=\frac{ -3\frac{ x-7 }{ x+3 }-7 }{ \frac{ x-7 }{ x+3 }-1 }\]
yeah i did that already
multiply by \(x-3\) what did you get in the numerator ?
why x-3?
typo i meant \(x+3\)
okay making sure ahha
-3(x-7)-7 is my numerator?
before distributing etc you should be looking at \[-3(x-7)-7(x+3)\]
forgot that distributive law didn't you?
ah yes
it is the distributive LAW, not the distributive option
hahaha yes so my numerator is:(-3x+21)-7x-21
numerator comes to -10x
got it perfect! thanks!
yw

Not the answer you are looking for?

Search for more explanations.

Ask your own question