Question

For the real-valued functions f(x)=2x+3 and g(x)=√x-5, find the composition fog and specify its domain using interval notation.

Answer 1

Find fog

• fog(x)
• f(g(x))
• f(√x-5)
• 2√(x-5)+3

For real range the domain

• x-5≥0
• x≥5

Domain is [5,oo)