Question 262924
How to find the inverse of one-to-one function bellow?
<pre><font size = 4 color = "indigo"><b>
f(x)=3x-5

The graph of that function is like this:

{{{drawing(400,400,-10,10,-10,10,

graph(400,400,-10,10,-10,10,3x-5) )}}}

{{{"f(x)"=3x-5}}}

Replace {{{"f(x)"}}} by {{{y}}}

{{{y=3x-5}}}

Interchange x and y

{{{x=3y-5}}}

Solve for y

{{{3y-5=x}}}

{{{3y=x+5}}}

{{{y=(x+5)/3}}}

Replace {{{y}}} by {{{f^(-1)}}}{{{(x)}}}

{{{f^(-1)}}}{{{(x)=(x+5)/3}}}

Now plot that on the same graph:

{{{drawing(400,400,-10,10,-10,10,
graph(400,400,-10,10,-10,10,3x-5)
graph(400,400,-10,10,-10,10,(x+5)/3) )}}}

Notice that the inverse is the reflection of the
original line in the "identity" line which has equation
{{{y=x}}}, called the identity line.  That's
the green dotted line below:

{{{drawing(400,400,-10,10,-10,10,
graph(400,400,-10,10,-10,10,3x-5)
graph(400,400,-10,10,-10,10,(x+5)/3,

x*sqrt(sin(6x))/sqrt(sin(6x))



) )}}}

Edwin</pre>