Question

Let f(x)=e^x and g(x)=x-3 what are the domain and range of (f g) (x)

Answer 1

Answer:

D. Domain: all rea numbers

Range: y >0

Step-by-step explanation:

Let f(x) =$e^x$

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)=$e^{x-3}$

(fg)(x)= $e^{x-3}$

Put x=0  then we get

$(fg)(0)= [tex]e^{0-3}$

(fg)(0)=$e^{-3}$

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

Answer 2

The domain and range of g are "all real numbers," so you want to find the range of f when its argument is from the set "all real numbers." That range is y > 0. The appropriate choice is
  D. domain: all real numbers; range: y > 0