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I need help! Please help me...
If F(x)=1/4.[(x+2)^2 -5], and F^-1(x) is the inverse of F(x).
(The F(x) is "x+2 all squared minus 5 all outside a quarter" Forgive my notation)
If A (is Greater than or equal to) -2.
What is F^-1(F(A))
(Reads the inverse function of the function of A)
probably A
The first guy to answer your thread is probably right.
A function is a rule that take an element from Set A to an element in set B. That is all a function does. It is a rule.
All that an Inverse function does is return the favor. If F(A)=B then F^-1(B)=A. In other words - If F maps A to B, then F^-1 maps B to A.
Now there is a catch. If F^-1 (f-inverse) is not a function then your question is unanswerable. So before you try to answer it, make sure your function F(x) is ONE-TO-ONE before you say that the answer is A
Later
mael
if the original function is not one-to-one, then you could draw a horizontal line for the graph of f(x) and it will intersect at more than one point. one way is to restrict the domain of the inverse of f(x) so that the inverse f-1(x) is also a function.
f(x) is a quadratic polynomial in x. This means that it is 1-to-1 and f^-1(x) always exists. Therefore f^-1(f(x)) = x under the given conditions.
umm yeah i mis-phrased my post. while a quadratic function is one-to-one, its inverse is not one-to-one. however if you restrict the domain to force it to be one-to-one (or split it into two functions). i think a bijective function will always have an one-to-one inverse (without any domain restrictions)
f-1(x) = sqrt(4x + 5) -2
=>There is an answer for for this so long as x >= -5/4. And there will always be two different answers, except when f(x) = -5/4 (or x = -2)
As A >= -2, f(A) >=5/4, so f(A) exits
=> f-1(f(a)) has two possible solutions, which are the same if A = -2
Forgive me if I'm wrong, but I understood one-to-one to mean that you can draw any vertical or horizontal line through a function, and it will never intersect the graph at more than one point. For a quadratic, a horizontal line would intersect a parabola twice in many places. Thus, parabolas are never one-to-one. However, they are one-to-many, which still qualifies as a function.