Respuesta :
The relation that is not a function, but whose inverse is a function are:
for every x in the domain of f, f -1[f(x)] = x, and
for every x in the domain of f -1, f[f -1(x)] = x
An inverse function is a characteristic that undoes the movement of another characteristic. A feature g is the inverse of a characteristic f if whenever y=f(x) then x=g(y). In different words, applying f and then g is the equal aspect as doing not anything. we are able to write this in terms of the composition of f and g as g(f(x))=x.
A few capabilities do not have inverse functions. for instance, remember f(x) = x2. There are numbers that f takes to four, f(2) = 4 and f(-2) = four. If f had an inverse, then the fact that f(2) = 4 might mean that the inverse of f takes four again to 2.
To discover the inverse function of an algebraic relation in terms of x and y, simply interchange the variables x and y, and resolve the equation for y. as an example, to discover the inverse of a relation y = x3, interchange x, and y after which clear up it for y. Then we get x = y3 ⇒ y = x1/3.
An inverse version can be represented by means of the equation xy=k or y=kx. this is, y varies inversely as x if there are a few nonzero steady k such that, xy=k or y=kx in which x≠0,y≠0 . assume y varies inversely as x such that xy=3 or y=3x.
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