What is the domain and range of the function
1 answer:
Answer:
Option d is correct.
Domain = all real number
range = positive real numbers
Step-by-step explanation:
Given the function:
Domain of the function is all real numbers except where the expression is undefined.
In this case, there is no real number that makes the expression undefined.
Domain of f(x) = = {a | a∈R}
Range is the set of all valid f(x) values.
Therefore, Domain is all real number and the range of function is positive real number
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Answer:
fog = 2√(x-1) + 1
Domain = [1, )
Step-by-step explanation:
Given the functions f(x)=2x+1 and g(x)=sqrt(x-1), we are to find the composite function fog
fog = f(g(x))
f(g(x)) = f(√(x-1))
f(√(x+1)) means that we are to replace variable x in f(x) with the function √(x-1)
f(√(x-1)) = 2(√(x-1))+1
f(√(x+1)) = 2√(x-1) + 1
fog = 2√(x-1) + 1
<em>For the function to exist on any real valued function, then the function inside square root i.e x-1 must be greater than or equal to zero (x-1≥0)</em>
If x-1≥0
x≥0+1
x≥1
This means the range of variable x must be values of x greater than or equal to 1.
Domain = [1, )