What are the domain and range of f(x) = 2(3x)? a. domain (-infinity, infinity), range (0,infinity) b. domain (-infinity, infinity) range (2,infinity) c. domain (0,infinity),range (-infinity, infinity)d. domain (2,infinity) range (-infinity. infinity)

Option A. Domain = (-Infinity, Infinity); Range (0, Infinity)

Solution:

f(x)=2^(3x)

a) This is an exponential function, and we don't have restrictions for the independent variable "x" in the exponent, then the Domain of f(x) is all the real numbers:

Domain f(x) = ( - Infinity, Infinity)

b) To find the range we can find the inverse function f^(-1) (x). The domain of the inverse function is the range of the original function f(x):

y=f(x)

y=2^(3x)

Isolating x: Applying log both sides of the equation:

log y = log 2^(3x)

Applying property of logarithm: log a^b = b log a; with a=2 and b=3x

log y = 3x log 2

Dividing both sides by 3 log 2:

log y / (3 log 2)=3x log 2 / (3 log 2)

log y / (3 log 2)=x

x=log y / (3 log 2)

Changing x by f^(-1) (x) and y by x:

f^(-1) (x) = log x / (3 log 2)

This is a logaritmic function and the argument of the logarithm must be greater than zero, then the Domain of the inverse function is:

x>0→Domain f^(-1) (x) = (0, Infinity)

The domain of the inverse is the range of the original function:

Range f(x) = Domain f^(-1) (x)

Range f(x) = (0, Infinity)

Domain f(x) = ( - Infinity, Infinity)

Range f(x) = ( 0, Infinity)

a. 74 degrees

step-by-step explanation:

because the lines through the side and the box in the corners shows that these are congruent triangles and since they are mirrored the 37 degrees is also mirrored so the answer is 37 * 2 which is 74.

y = x + 95

y = 42 + 95

y=137 mm hg