Question

What are the domain and range of the function
$f(x) = 4( \sqrt[3]{81} ) ^{x}$
A) {x| x is a real number}; {y|y>0}

B) {x| x>4}; {y|y>0}

C) {x| x is a real number}; {y|y>4}

D) {x|x>4}; {y|y>4}

Answer 1

We have the following function:
 f (x) = 4 * ((81) ^ (1/3)) ^ x
 We observed that:
 (81) ^ (1/3) = 4.326748711> 1
 Therefore the function grows as it increases and decreases as x decreases.
 We have then:
 Domain: all reals.
 Range: all reals greater than zero.
 Answer:
 A) {x | x is a real number}; {y | y> 0}