Question

For the real-valued functions f(x)=2x+1 and g(x)=sqrt(x-1), find the composition f o g and specify its domain using interval notation.

Answer 1

Answer:

fog = 2√(x-1) + 1

Domain = [1, $\infty$)

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, $\infty$)