Given the functions, f(x) = 5x2 - 3x + 1 and g(x) = 2x2 + x - 2, perform the indicated operation. When applicable, state the domain restriction.(f - g)(x)

Given the functions, f(x) = x3 + x2 + 1 and g(x) = -6x2 + 2, perform the indicated operations. When applicable, state the domain restriction.(f + g)(x)x3 + 7 x2 + 3x3 - 7 x2 + 5x3 - 5 x2 + 3x3 + 5 x2 + 3

Find the functions and their domains. (Enter the domains in interval notation.)f(x) = x + 1x,    g(x) = x + 5x + 2(a)    f ∘ g(f ∘ g)(x)  = 2x2+14x+29(x+2)(x+5)​ domain    (−∞,−5)∪(−5,−2)∪(−2,∞) (b)    g ∘ f(g ∘ f)(x)  = domain    (c)    f ∘ f(f ∘ f)(x)  = domain    (d)    g ∘ g(g ∘ g)(x)  = domain

The domain of the function f(x) is open square bracket, 20, comma, infinity, right bracket[20,∞) and the range is open square bracket, minus, 16, comma, minus, 2, close square bracket[−16,−2]. Using interval notation, find the domain and range of g, of, x, equals, f, of, 5, xg(x)=f(5x).

Find (f ◦ g)(x), (g ◦ f )(x), domain and range of (f ◦ g)(x).(a) f (x) = 2x + 4, g(x) = 3x − 5(b) f (x) = √x + 2, g(x) = 2x − 4(c) f (x) = 1x , g(x) = 1x(d) f (x) = x2, g(x) = x − 3(e) f (x) = x2 + 2, g(x) = √x − 4

Let f (x) = √x − 1 and g(x) = 1x − 2 .(i) State the domains for f and g, and the range of f .