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 and g(x) = -7x-8/x-1

Answer 1

f(g(x)) = f (-7x-8/x-1) Subs this value of x in the equation (f(x) = x-8/x+7)and see ...

Answer 2

What??

Answer 3

An inverse is when you replace X with Y...
For example, the inverse of y = 3x is x = 3y (Thus x/3 = y)
For this question, find the inverse of f(x), and your answer should equal g(x).

Answer 4

f(x) = x-8/x+7


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

Answer 5

And Proceed Same as this for g(f(x))

Answer 6

your job is to compute
\[f\circ g(x)\] first step is
\[f\circ g(x)=f(g(x))=f(\frac{-7x-8}{x-1})\]
\[=\frac{\frac{-7x-8}{x-1}-8}{\frac{-7x-8}{x-1}+7}\]
then simplify this ugly compound fraction
start by multiplying to and bottom by \(x-1\)
you will have a whole orgy of cancellation, leaving nothing but \(x\)

Answer 7

can you please explain to me how to do the g(f(x) because i am not seeing how i can plug it in to prove it?

Answer 8

\[g(f(x))=g(\frac{x-8}{x+7})\] is as start

Answer 9

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

Answer 10

that is, replace the input by \(\frac{x-8}{x+7}\)
now it is algebra from here on in
ugly algebra, but algebra just the same

Answer 11

thank you so much!!