[MOVED] Composition and Inverses of Functions

[Tigertigre2000]

I. For f(x) = x/(x + 4) and g(x) = -4/(2x - 1):
(a) Find the inverse of f(x).
(b) Prove that your inverse is correct.
(c) Find f(g(x)) in simplified form, listing correct restrictions of x. Check your restrictions with a calculator but not in simplified form.

(a) x = y/(y + 4)
. . .x= -4 ??

(b) How would you prove it?
(c) f(-4/(2x - 1))
. . .=(-4/(2x - 1))/ (-4/(2x - 1) + 4)

How would you simplify this more?

I would really appreciate your help.

 

[stapel]

a) The usual process for finding an inverse is as follows:

. . . . .Rename "f(x)" as "y".
. . . . .Switch "x" and "y".
. . . . .Solve for "y=".
. . . . .Rename the new "y" as "f^-1(x)".

You appear to have done the first and second steps. I don't know where "x = -4" came from...? Now you need to solve "x = y/(y + 4)" for "y=". A good first step would be to multiply through by y + 4. Then get all the y-containing terms together on one side, factor out the y, and divide off whatever is left, to get y by itself.

b) To prove two functions, f(x) and h(x), are inverses, you compose them. If f(h(x)) = h(f(x)) = x, then the functions are inverses.

c) For a start, you could work on getting common denominators. (I don't know what method you learned for simplifying complex fractions, but now would be the time to apply that method.)

Eliz.

 

[Tigertigre2000]

Thanks for the help

You make it sound so easy.
Thanks for your quick reply.