f(x) = 4x³ + 3 a) Show that f(x) has an inverse, i.e. there exists a function g(x) such that g(f(x)) = x. b) Find g(x) c) Find g'(x)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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### Problem 1:

Given: \( f(x) = 4x^3 + 3 \)

#### a) Show that \( f(x) \) has an inverse, i.e. there exists a function \( g(x) \) such that \( g(f(x)) = x \).

#### b) Find \( g(x) \).

#### c) Find \( g'(x) \).
Transcribed Image Text:### Problem 1: Given: \( f(x) = 4x^3 + 3 \) #### a) Show that \( f(x) \) has an inverse, i.e. there exists a function \( g(x) \) such that \( g(f(x)) = x \). #### b) Find \( g(x) \). #### c) Find \( g'(x) \).
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