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## Find two functions f(x) and g(x) such that f(g(x)) = x but g(f(x)) does not = x.?

I had trouble with this as well, but with a few hints from my teacher, I eventually figured it out.

Using square roots and negatives, I came up with these two equations:

f(x)=-(x^2)

g(x)=-sqrt(x)

Note that both equations have a negative in the front. When you plug these into f(g(x)) and g(f(x)), you get:

f(g(x))=-(-(sqrt(x))^2 …………………The square root and square cancel out, leaving:

=-(-x) ………………….which simplifies to:

=x

Now for g(f(x)):

g(f(x))=-(sqrt(-(x^2))) …………………This doesn t simplify anymore than this since whatever

you square for x will end up being negative anyway.

Even though the original post was quite a while ago, I hope this helps anyone in the future!

Source(s): Hints from my teacher and my brain slowly, but eventually, piecing it together.

Composition of Functions – MATH – It is important to get the Domain right, or we will get bad results! Domain of Composite Function. We must get both Domains right (the composed function and the first function used).. When doing, for example, (g º f)(x) = g(f(x)): Make sure we get the Domain for f(x) right,; Then also make sure that g(x) gets the correct Domain2. (a) Find an example of two functions f(x) and g(x), such that lim x→0 [f(x) · g(x)] exists (and is finite), but lim x→0 f(x) does not exist. (b) Find an example of two functions f(x) and g(x), such that lim x→0 f(x) = 0, but lim x→0 [f(x) · g(x)] ≠ 0 .Find two functions f(x) and g(x) such that f(g(x)) = x but g(f(x)) does not = x.? This has me stumped. Seems like in most situations you can prove that a function is an inverse of another by proving (g(x)) = x and g(f(x)) = x. I'm trying to find examples of ones where this is not true. Thanks in advance.

Solved: 2. (a) Find An Example Of Two Functions F(x) And G – Free functions composition calculator – solve functions compositions step-by-step This website uses cookies to ensure you get the best experience. By using this website, you agree to our Cookie Policy.Sometimes you have to be careful with the domain and range of the composite function. Given f (x) = sqrt(x) and g(x) = x – 2, find the domains of (f o g)(x) and (g o f)(x).; Since f (x) involves a square root, the inputs have to be non-negative. This means that the domain (the set of x-values) for f (x) is "all x > 0".In this video we learn about function composition. Composite functions are combinations of more than one function. In this video we learn about f(g(x)) and g…

Find two functions f(x) and g(x) such that f(g(x)) = x but – URGENT: Find two functions f(x) and g(x) such that f[g(x)] =x but g[f(x)] does not equal x. Get the answers you need, now!Graphically, f(x) and f-1 (x) are related in the sense that the graph of f-1 (x) is a reflection of f(x) across the line y = x.Recall that the line y = x is the 45° line that runs through quadrants I and III. In addition, if f and f-1 are inverse functions, the domain of f is the range of f-1 and vice versa. If the point (a, b) lies on the graph of f, then point (b, a) lies on the graph of f-1.In mathematics, function composition is an operation that takes two functions f and g and produces a function h such that h(x) = g(f(x)).In this operation, the function g is applied to the result of applying the function f to x.That is, the functions f : X → Y and g : Y → Z are composed to yield a function that maps x in X to g(f(x)) in Z.. Intuitively, if z is a function of y, and y is a