Let ƒ : ℝ → ℝ be continuously differentiable function and k > 0 be a number such that ƒ '(x) ≥ k for all x ∈ R. Show ƒ is one-to-one and onto, and has a continuously differentiable inverse ƒ - 1 : ℝ → ℝ.
Let ƒ : ℝ → ℝ be continuously differentiable function and k > 0 be a number such that ƒ '(x) ≥ k for all x ∈ R. Show ƒ is one-to-one and onto, and has a continuously differentiable inverse ƒ - 1 : ℝ → ℝ.
Let ƒ : ℝ → ℝ be continuously differentiable function and k > 0 be a number such that ƒ '(x) ≥ k for all x ∈ R. Show ƒ is one-to-one and onto, and has a continuously differentiable inverse ƒ - 1 : ℝ → ℝ.
Let ƒ : ℝ → ℝ be continuously differentiable function and k > 0 be a number such that ƒ '(x) ≥ k for all x ∈ R. Show ƒ is one-to-one and onto, and has a continuously differentiable inverse ƒ - 1 : ℝ → ℝ.
With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.
Expert Solution
Step 1
Let me show f is one one first,then onto then continuously differentiable....
