Answer with Step-by-step explanation:
Since we have given that
a. f: ℝ → ℝ given by f(x) = x + 2
Domain would be all real numbers i.e. (-∞, ∞)
Range would be all real numbers i.e. (-∞, ∞)
b. g: ℝ → ℝ given by g(x) = √x − 1
Domain would be all positive numbers i.e. [0,∞)
Range would be [-1,∞)
c. f(g(x))
[tex]f(g(x))=f(\sqrt{x}+1)=\sqrt{x}+1+2=\sqrt{x}+3[/tex]
Domain would be [0,∞)
Range would be [3,∞)
d. g(f(x))
[tex]g(x+2)=\sqrt{x+2}-1[/tex]
Domain would be [-2,∞)
Range would be (0,∞)
