\[charlottecain said:Temperatures can be converted from Fahrenheit to Celsius using the
function $f(x) = \frac59(x − 32)$.
(a) Calculate $f(59)$.
To find the inverse of $f$ you need to solve the equation $y=\frac59(x − 32)$ for $x$, i.e., express $x$ through $y$. Can you do this? Start by multiplying both sides by $\frac95$.charlottecain said:(b) Find $f^{-1}(x)$, and verify that $f^{-1}(f(59)) = 59$.
To do this you need to solve the equation $\frac59(x − 32)=x$. Can you do this?charlottecain said:(c) Let K be the set {x : f(x) = x}. Find all elements of K and list K
A set is a collection of distinct objects or elements. These elements can be anything, such as numbers, letters, or even other sets. Sets are typically represented by curly brackets, and each element is separated by a comma.
Two sets are considered equal if they have the same elements. This means that every element in one set is also present in the other set, and vice versa. The order of the elements does not matter when determining equality.
An inverse function is a function that "undoes" another function. It is essentially a reversal of the original function, where the input and output values are swapped. Inverse functions are represented by f^-1(x).
To find the inverse of a function, you can use the following steps:
No, not all functions are invertible. For a function to have an inverse, it must be one-to-one, meaning that each input has only one corresponding output. Functions that fail the horizontal line test, where a horizontal line intersects the graph of the function more than once, are not invertible.