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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

User LIH
by
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2 Answers

5 votes

Answer:

D. Domain: all rea numbers

Range: y >0

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

User Dwerner
by
8.3k points
6 votes
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
User Abhishek Pankar
by
7.7k points

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