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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) ?


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

functions inverse prob.jpg

Taken from HiSet free practice test


Staff member
Feb 24, 2012
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:

\(\displaystyle y=x\)