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If f(x) and g(x) are inverse functions, in which line will g(x) be a reflection of f(x) ?

pan90

New member
Jul 30, 2019
4
Can anyone explain the logic behind the answer?

functions inverse prob.jpg

Taken from HiSet free practice test
 

MarkFL

Pessimist Singularitarian
Staff member
Feb 24, 2012
13,666
St. Augustine, FL.
Suppose we have the point:

\(\displaystyle (x,f(x))\)

on the plot of \(f(x)\). Then, on the plot of \(g(x)\), we must have the corresponding point:

\(\displaystyle (f(x),x)\)

Now, consider that for all possible points, the locus of the mid-points is:

\(\displaystyle \left(\frac{x+f(x)}{2},\frac{x+f(x)}{2}\right)\)

Thereby implying that the line of symmetry must be:

\(\displaystyle y=x\)