Let f(x) and g (x) be one-to-one functions, and let h (x) = g ( f(x)). Show that the inverse functionof h (x) is h^−1 (x) = f^ −1(g^−1 (x))

) Let f, g be differentiable functions on an interval I. Suppose that a, b ∈ Iwith f (b) ≥ g(b) and f ′(x) ≤ g′(x) on [a, b]. Show that f (x) ≥ g(x) on[a, b].

Let  and g be the inverse of f, then value of g'(0) is .Reason (R) : If g(x) is inverse of f(x), then g(f(x)) = x.

In (a)–(d), determine whether f and g are inverse functions.(a) f(x) = 4x, g(x) = 14 x

Let f, g : R → R be given functions. Suppose that f and g are continuous at c ∈ R.Prove that the functionl(x) := inf{f (x), g(x)}, x ∈ R,is continuous at c.

Consider the functions f , g : R → R defined as f (x) = 3px + 1 and g(x) = x3. Find theformulas for g ◦ f and f ◦ g