Question

Confirm that f and g are inverses by showing that f(g(x)) = x and g(f(x)) = x. f(x) = (x-8)/(x+7) g(x)= (-7x-8)/(x-1)

Answer 1

@bridgetx516x @timo86m

Answer 2

@abb0t @beketso @Chooch146 @drummerboyrevived @emily2013 @farmergirl411 @Giovanni @help123please. @Meepi

Answer 3

@Mertsj @Milani123

Answer 4

Someone PLz Help

Answer 5

first

f(g(x)) = f((-7x-8)/(x-1)) meaning where u see x in the expression of f u replace it with ((-7x-8)/(x-1))

Answer 6

i already found f(g(x)) i cant find g(f(x))

Answer 7

ok.give a minute

Answer 8

@Chooch146 help plz

Answer 9

@zepdrix

Answer 10

Can you find the f (g(x))?

Answer 11

i already have

f((-7x-8/x-1) =
[ (-7x-8)/(x-1) - 8 ] / [ (-7x-8)/(x-1) + 7 ] =
-15x/-15 = x

Answer 12

\[f(g(x))=\frac{\frac{-7x-8}{x-1}-8}{\frac{-7x-8}{x-1}+7}\times \frac{x-1}{x-1}\frac{-7x-8-8(x-1)}{-7x-8+7(x-1)}\]

Answer 13

=
\[\frac{-7x-8-8x+8}{-7x-8+7x-7}=\frac{-15x}{-15}=x\]

Answer 14

So we have shown that the f(g(x))=x. Now we must show that the g(f(x))=x

Answer 15

ok. thats is the one i can't show

Answer 16

@Mertsj could u help me show g(f(x)) PLZ???

Answer 17

\[g(f(x))=\frac{-7\times\frac{x-8}{x+7}-8}{\frac{x-8}{x+7}-1}\times\frac{x+7}{x+7}=\frac{-7(x-8)-8(x+7)}{x-8-1(x+7)}\]

Answer 18

Can you finish it now?

Answer 19

would the answer be 15? @Mertsj

Answer 20

I believe that your instructions say that the g(f(x))=x

Answer 21

then i must have finished it wrong. where did i mess up

Answer 22

Post what you did and I will see.

Answer 23

x-8 cancels out and x-7 cancels out which gives you -7-8/-1
which leaves you with 15

Answer 24

@Mertsj

Answer 25

x-8 does not cancel out. Only factors can be cancelled.

Answer 26

What is -7(x-8)

Answer 27

-7x+56 @Mertsj

Answer 28

What is -8(x+7)?

Answer 29

-8x -56 @Mertsj

Answer 30

So the numerator: -7(x-8)-8(x+7)=-7x+56-8x-56

Answer 31

Simplify that some more.

Answer 32

-15x

Answer 33

So the numerator is -15x. Now do the denominator

Answer 34

denominator is 15

Answer 35

Try again

Answer 36

than k u for walking me thru this!!!!!

Answer 37

-15 sorry

Answer 38

What is the denominator?

Answer 39

So now we have:
\[\frac{-15x}{-15}\]

Answer 40

What does that equal?

Answer 41

x

Answer 42

So now we have shown that f(g(x))=x
And g(f(x))=x
And that is the definition of inverse functions so we have shown that f and g are indeed inverse functions.

Answer 43

THANK U

Answer 44

yw