Let f(x)=e^x and g(x)=x-3 what are the domain and range of (f g) (x) a. domain: x> 0 range: y< 0 b. domain: x> 3 range y> 0 c. domain: al real numbers range: y< 0 d. domain: all real numbers range: y> 0

D. Domain: all rea numbers

Range: y >0

Step-by-step explanation:

Let f(x) =

Domain of function f(x) : all real numbers because it is define for every real number.

Range of function f(x) y >0 because exponential function can never  be zero.

g(x)=x-3

Domain of g(x) : all real numbers

Range g(x): all real numbers.

(fg)(x)= f(g(x))

f(x-3)=

(fg)(x)=

Put x=0  then we get

(fg)(0)=

Domain of (fg)(x) is the set of real numbers because it is define for every real number.

Exponential function can never be zero .

Function (fg)(x) can never be zero it is always greater than zero because it is an exponential function

Therefore , the range of (fg)(x) is greater than zero.

Hence, option D  is correct .

Domain: all real numbers

Range: y >0

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