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Question Number 31673 by gunawan last updated on 12/Mar/18
![let function−function f and g continues [ a, b] and diferensiabel (a, b). If f′(x)=g′(x)≠0, ∀x ∈ (a, b) and g(a)=a, g(b)=b, find value ∣f(b)−f(a)∣.](Q31673.png)
$$\mathrm{let}\:\mathrm{function}−\mathrm{function}\:{f}\:\mathrm{and}\:{g} \\ $$$$\mathrm{continues}\:\left[\:{a},\:{b}\right]\:\mathrm{and}\:\mathrm{diferensiabel} \\ $$$$\left({a},\:{b}\right).\:\mathrm{If}\:{f}'\left({x}\right)={g}'\left({x}\right)\neq\mathrm{0},\:\forall{x}\:\in\:\left({a},\:{b}\right) \\ $$$$\mathrm{and}\:{g}\left({a}\right)={a},\:{g}\left({b}\right)={b},\:\mathrm{find}\:\mathrm{value} \\ $$$$\mid{f}\left({b}\right)−{f}\left({a}\right)\mid. \\ $$