Consider the function

MATHEMATICS · Subjective · AP · AP Precalculus · Exponential and Logarithmic Functions · Exponential and Logarithmic Functions

Problem

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

. (i) Show that

g

is one–one and hence has an inverse. (ii) Find

g^{-1}(x)

in simplest form. (iii) Determine the domain and range of

g^{-1}

. (iv) Find the

x

–intercept of

g^{-1}

and interpret its meaning with reference to the graph of

g