a.) For the function to have an inverse, it must be $\underline{\text{a one to one function}}$. So, which one of the following functions has an inverse?
$f(x) = x^2 \qquad g(x) = x^3$
b.) What is the inverse of the function you chose in part (a).
a.) Since, the function $f(x) = x^2$ is increasing and is symmetric to $y$-axis, then if you use horizontal line test, the function will intersect the line more than once, that's why $f(x) = x^2$ is not one to one. On the other hand, $g(x) = x^3$ is increasing and is symmetric to origin, that's why it has an inverse. Thus, $g(x) = x^3$ is one to one.
b.) To find the inverse, first, we write $y = g(x)$
$y = x^3$
Then solve for $x$,
$
\begin{equation}
\begin{aligned}
x =& \sqrt[3]{y}
\qquad \text{Interchange $y$ and $x$}
\\
\\
y =& \sqrt[3]{x}
\end{aligned}
\end{equation}
$
Thus, the inverse of $g(x) = x^3$ is $h(x) = x^{\frac{1}{3}}$
Thursday, September 12, 2019
College Algebra, Chapter 3, 3.7, Section 3.7, Problem 2
Subscribe to:
Post Comments (Atom)
Why is the fact that the Americans are helping the Russians important?
In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...
-
There are a plethora of rules that Jonas and the other citizens must follow. Again, page numbers will vary given the edition of the book tha...
-
The only example of simile in "The Lottery"—and a particularly weak one at that—is when Mrs. Hutchinson taps Mrs. Delacroix on the...
-
A good thesis statement presents a claim (an interpretive stance on a story that can be defended using textual evidence) and is a position w...
-
The given two points of the exponential function are (2,24) and (3,144). To determine the exponential function y=ab^x plug-in the given x an...
-
What does the hot air balloon symbolize? To the Assad son who buys the hot air balloon, it symbolizes a kind of whimsy that he can afford. B...
-
The play Duchess of Malfi is named after the character and real life historical tragic figure of Duchess of Malfi who was the regent of the ...
-
Allie’s baseball mitt is extremely important to Holden in The Catcher in the Rye. It is a symbol of Allie since it was important to his brot...
No comments:
Post a Comment