What are the domain and range of the function f(x) = 4(3 square root 81)^x? {x| x is a real number}; {y| y > 0}{x| x > 4}; {y| y > 0}{x| x is a real number}; {y| y > 4}{x| x > 4}; {y| y > 4}

we are given

Domain:

we know that domain is all possible values of x for which any function is defined

Here , since, x is only exponent

so, we can take any values of x

it will be defined for all values of x

so, domain is all real numbers

{x | x is a real number}

Range:

we know that

range is all possible values of f(x) or y

Since, there is no negative sign here

so, f(x) will always be positive and greater than 0

so, range is y>0

{x| x is a real number}; {y| y>0}

Step-by-step explanation:

use the power rule  

( a b ) n = a n b n

to distribute the exponent.

apply the product rule to  

3 x 2 y 3 . ( 3 x 2 ) 2 ( y 3 ) 2

apply the product rule to  

3 x 2 . 3 2 ( x 2 ) 2 ( y 3 ) 2

raise  

3

to the power of  

2 . 9 ( x 2 ) 2 ( y 3 ) 2 multiply the exponents in   ( x 2 ) 2

.

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 2 ⋅ 2 ( y 3 ) 2

multiply  

2   by   2 . 9 x 4 ( y 3 ) 2

multiply the exponents in  

( y 3 ) 2 .

apply the power rule and multiply exponents,  

( a m ) n = a m n . 9 x 4 y 3

⋅

2

multiply  

3   by   2 . 9 x 4 y 6

step-by-step explanation:

(- 1, 0 )

step-by-step explanation:

an x- intercept is where the function crosses the x- axis.

to find the x- intercept/s look for the value of x when f(x) = 0

from the given table there are 3 values of x where f(x) = 0

when x = - 1, x = 2, x = 3

the one that is listed is (- 1, 0 )