Consider the function

MATHEMATICS · Multi-part · A Level · Mathematics · Exponentials and logarithms · Exponentials and logarithms

Problem

h(x)=a^{x-2}+1

, where

0<a<1

. Answer the following, giving full justification: (i) Determine the domain of

h

and write the equation of every asymptote of its graph. (ii) Find the range of

h

. (iii) Calculate the

y

-intercept of the graph of

h

and decide whether the graph possesses an

x

-intercept. Give reasons. (iv) Prove that

h

is a decreasing function on its entire domain. (v) Solve the equation

h(x)=2

for

x