F(x)=squarerut of x+2,g(x)=xsquare+1 then find fog,gof,fof and gog

Please calculat this queation

ever hear of using actual math notation?

f(x) = √(x+2)
g(x) = x^2 + 1
(f◦g)(x) = f(g) = √(g+2) = √(x^2+1 + 2) = √(x^2+3)
(g◦f)(x) = g(f) = f^2 + 1 = x+2 + 1 = x+3
now do the others in like wise

Did you know?

Did you know that in mathematics, compositions of functions, denoted as f ◦ g (f of g) and g ◦ f (g of f), can give us interesting insights? For example, given the functions f(x) = √(x+2) and g(x) = x^2+1, we can evaluate their compositions: fog, gof, fof, and gog. When we substitute g(x) into f(x), fog represents the composition of f with g. Thus, fog(x) = f(g(x)) = f(x^2+1). On the other hand, gof represents the composition of g with f. Hence, gof(x) = g(f(x)) = g(√(x+2)). Moreover, fof stands for the composition of f with itself. Consequently, fof(x) = f(f(x)) = f(√(x+2)). Lastly, gog signifies the composition of g with itself. Thus, gog(x) = g(g(x)) = g(x^2+1). Exploring these compositions can provide us with new mathematical representations and deepen our comprehension of functions.