SOLUTION: Determine the value of k so that the function {{{f(x)=(x-6)/(2x+k)}}} will be its own inverse.

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Question 1196503: Determine the value of k so that the function will be its own inverse.
Found 3 solutions by josgarithmetic, MathLover1, ikleyn:
Answer by josgarithmetic(39618)   (Show Source):
You can put this solution on YOUR website!
If find the inverse for f(x), then, according to wanted conditions,

and maybe this equation would help.

If try to work through this equation, you may find this equivalent:

, and you can compare the corresponding parts, and......, ....

Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website!

Determine the value of k so that the function will be its own inverse.

inverse function is :

recall that

.........swap variables
.........solve for

so, inverse is
’ =

now equal and ’

.......quadratics will be equal if and only if corresponding coefficients are equal

then
=>
=>

and your function is:

and will be its own inverse

Answer by ikleyn(52792)   (Show Source):
You can put this solution on YOUR website!
.

            I will show you non-standard way to solve this problem, which is much faster and much easier.

Let's calculate f(0), i.e. the value of function f at x= 0. It is f(0) = = . Thus we know that function f maps 0 (the zero) to . Hence, the inverse function should map to 0 (zero), and we want the inverse function would be the same formula as the direct function. In other words, we want f(-6/k) = 0, which means = 0. In order for this multi-store fraction would be zero, it is necessary and sufficient that its numerator be zero = 0, which gives -6 - 6k = 0, or -6 = 6k k = = -1. ANSWER. k = -1.

Solved.