Consider the function defined by

MATHEMATICS · Subjective · CBSE · Mathematics · Relations and Functions · Relations and Functions

Problem

Consider the function

f:\mathbb R\to(1,\infty)

defined by

f(x)=2^{3x-4}+1

. (i) Find the inverse function

f^{-1}(x)

and write down its domain and range. (ii) Verify that

f\bigl(f^{-1}(x)\bigr)=x

for every permissible

x

. (iii) Determine all real numbers

x

which satisfy

f(x)=f^{-1}(x)

, i.e. find the coordinates of the point(s) where the graphs of

y=f(x)

and

y=f^{-1}(x)

intersect.