Answer:
fog = 2√(x-1) + 1
Domain = [1, [tex]\infty[/tex])
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
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)
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, [tex]\infty[/tex])
