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- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_370%3A_Precalculus/05%3A_Further_Topics_in_Functions/5.02%3A_Inverse_FunctionsThinking of a function as a process like we did in Section 1.4, in this section we seek another function which might reverse that process. As in real life, we will find that some processes (like putti...Thinking of a function as a process like we did in Section 1.4, in this section we seek another function which might reverse that process. As in real life, we will find that some processes (like putting on socks and shoes) are reversible while some (like cooking a steak) are not. We start by discussing a very basic function which is reversible, ()=3+4 f ( x ) = 3 x + 4 . Thinking of f as a process, we start with an input x and apply two steps, as we saw in Section 1.4
- https://math.libretexts.org/Bookshelves/Precalculus/Precalculus_(Stitz-Zeager)/05%3A_Further_Topics_in_Functions/5.04%3A_Other_Algebraic_FunctionsThinking of a function as a process like we did in Section 1.4, in this section we seek another function which might reverse that process. As in real life, we will find that some processes (like putti...Thinking of a function as a process like we did in Section 1.4, in this section we seek another function which might reverse that process. As in real life, we will find that some processes (like putting on socks and shoes) are reversible while some (like cooking a steak) are not. We start by discussing a very basic function which is reversible, ()=3+4 f ( x ) = 3 x + 4 . Thinking of f as a process, we start with an input x and apply two steps, as we saw in Section 1.4
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_372%3A_College_Algebra_for_Calculus/05%3A_Further_Topics_in_Functions/5.02%3A_Inverse_FunctionsThinking of a function as a process like we did in Section 1.4, in this section we seek another function which might reverse that process. As in real life, we will find that some processes (like putti...Thinking of a function as a process like we did in Section 1.4, in this section we seek another function which might reverse that process. As in real life, we will find that some processes (like putting on socks and shoes) are reversible while some (like cooking a steak) are not. We start by discussing a very basic function which is reversible, ()=3+4 f ( x ) = 3 x + 4 . Thinking of f as a process, we start with an input x and apply two steps, as we saw in Section 1.4
- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_(Stitz-Zeager)_-_Jen_Test_Copy/05%3A_Further_Topics_in_Functions/5.04%3A_Other_Algebraic_FunctionsBy interpreting $x^{2/3}$ as $\sqrt[3]{x^2}$ we have $\sqrt[3]{x^2} = -2$ or $\sqrt[3]{x^2}= 3$. Cubing both sides of these equations results in $x^2 = -8$, which admits no real solution, or $x^2 = 27...By interpreting $x^{2/3}$ as $\sqrt[3]{x^2}$ we have $\sqrt[3]{x^2} = -2$ or $\sqrt[3]{x^2}= 3$. Cubing both sides of these equations results in $x^2 = -8$, which admits no real solution, or $x^2 = 27$, which gives $x = \pm 3 \sqrt{3}$. We construct a sign diagram and find $x^{4/3} - x^{2/3} - 6 > 0$ on $\left(-\infty, -3 \sqrt{3}\right)\cup \left(3 \sqrt{3}, \infty\right)$. To check our answer graphically, we set $f(x) = x^{2/3}$ and $g(x) = x^{4/3}-6$. The solution to $x^{2/3} < x^{4/3} - 6$ …
- https://math.libretexts.org/Courses/Cosumnes_River_College/Math_384%3A_Foundations_for_Calculus/03%3A_Functions_-_Advanced_Concepts_for_Calculus/3.02%3A_Inverse_FunctionsThinking of a function as a process like we did in Section 1.4, in this section we seek another function which might reverse that process. As in real life, we will find that some processes (like putti...Thinking of a function as a process like we did in Section 1.4, in this section we seek another function which might reverse that process. As in real life, we will find that some processes (like putting on socks and shoes) are reversible while some (like cooking a steak) are not. We start by discussing a very basic function which is reversible, ()=3+4 f ( x ) = 3 x + 4 . Thinking of f as a process, we start with an input x and apply two steps, as we saw in Section 1.4
- https://math.libretexts.org/Courses/Lorain_County_Community_College/Book%3A_Precalculus_Jeffy_Edits_3.75/05%3A_Further_Topics_in_Functions/5.04%3A_Other_Algebraic_FunctionsBy interpreting $x^{2/3}$ as $\sqrt[3]{x^2}$ we have $\sqrt[3]{x^2} = -2$ or $\sqrt[3]{x^2}= 3$. Cubing both sides of these equations results in $x^2 = -8$, which admits no real solution, or $x^2 = 27...By interpreting $x^{2/3}$ as $\sqrt[3]{x^2}$ we have $\sqrt[3]{x^2} = -2$ or $\sqrt[3]{x^2}= 3$. Cubing both sides of these equations results in $x^2 = -8$, which admits no real solution, or $x^2 = 27$, which gives $x = \pm 3 \sqrt{3}$. We construct a sign diagram and find $x^{4/3} - x^{2/3} - 6 > 0$ on $\left(-\infty, -3 \sqrt{3}\right)\cup \left(3 \sqrt{3}, \infty\right)$. To check our answer graphically, we set $f(x) = x^{2/3}$ and $g(x) = x^{4/3}-6$. The solution to $x^{2/3} < x^{4/3} - 6$ …
