Watched the lesson 3 times and still don't understand this..... If h(x) is the inverse of f(x), what is the value of h(f(x))

Question

Watched the lesson 3 times and still don't understand this.  I am retaking this class in summer school and feel completely lost.  Please help..... If h(x) is the inverse of f(x), what is the value of h(f(x))

Answer 1

Hi Joseph,

 

First of all, get un-lost (that's an attitude, you know).

 

The notation f(x) and h(x) indicate functions.  A function produces, at most, one value for each input value.  Thus, if

   y = f(x),   y passes the "vertical line test" (at most one value of y on that line for each allowable value of x.

 

Once we have a function f(x0, we often represent the inverse function as g(x) or h(x).  The inverse function is still a function, but it goes in reverse -- for each value of y, there is at most one value of x.

 

Before solving this problem, let's think of an example:  y =2x is a function.  If I give you a value of x (say, 2), you can tell me the value of y (it's 4).  The inverse does this in reverse order:  I give you the value 4, and you tell me what x produced it (I hope you say 2).

 

O.K., the problem  The problem states that f(x) is the function and that h(x) is the inverse of f(x).  Reread the problem statement until you agree with that.

 

So, f(x) produced a result (we called it y before).  Now, we want to know what x value produced that y.  The notation used is h(f(x) which is called the inverse.  It's still a function, but it goes in reverse.  The value that produced f(x) when the input value was x, was just x.  That means h(f(x) = x.

 

Boy, this sounds like double-talk and I'm writing it! 

Answer 2

If a function f maps a value from A to B, then by definition the inverse function maps B back to A.  

 

So h(f(A)) = h(B) = A for all value of A in the domain of f.  

 

In other words, h(f(x)) = x.  

 

The function and its inverse cancel each other out, leaving you with the original value.