The function is defined by .

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

Problem

The function

h

is defined by

h(x)=-\dfrac12\;4^{\,x+1}+2

. (i) Find the domain of

h

. (ii) Determine the range of

h

. (iii) State the interval(s) on which

h

is increasing and the interval(s) on which it is decreasing, giving reasons for your answer.