Question

Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = x^3 + 3x^2$. a) Show that $f$ is 1-1 or find a counterexample. b) Show that $f$ is onto or find a counterexample.

          Let $f: \mathbb{R} \to \mathbb{R}$ be defined by $f(x) = x^3 + 3x^2$.
a) Show that $f$ is 1-1 or find a counterexample.
b) Show that $f$ is onto or find a counterexample.

Let f: ℝ→ℝ be defined by f(x) = x^3 + 3x^2.
a) Show that f is 1-1 or find a counterexample.
b) Show that f is onto or find a counterexample.

Added by Alison L.

Calculus Early Transcendentals

Howard Anton, Irl Bivens, Stephen Davis 9th Edition

Chapter 3

Instant Answer

Solved by Expert Joseph David

Step 1

Let's assume that f(x1) = f(x2) for some x1 and x2. Then we have: x1^3 + 3x1^2 = x2^3 + 3x2^2 Rearranging the equation, we get: x1^3 - x2^3 + 3x1^2 - 3x2^2 = 0 Factoring the equation using the difference of cubes formula, we have: (x1 - x2)(x1^2 + x1x2 + Show more…

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Can someone help me with Part B? Thank you. Let f: IR -> R be defined by f(x) = x^3 + 3x^2. a) Show that f is 1-1 or find a counterexample. b) Show that f is onto or find a counterexample.