The process of finding the inverse in mathematics involves identifying a function that effectively undoes the operation of the initial function. To put it simply, if a function transforms 'x' into 'y', then its inverse function reverts 'y' back to 'x'. This is symbolized as f^-1(x) and is a vital step in resolving a range of mathematical challenges.
| Topic | Problem | Solution |
|---|---|---|
| None | The following functions are inverses of each othe… | Given two functions $f(x)=5 x-9$ and $g(x)=\frac{x+9}{5}$, we are asked to determine if they are in… |
| None | The one-to-one functions $g$ and $h$ are defined … | The first question asks for the inverse of function g at 5. This means we need to find the x-value … |
| None | For the function $y=f(x)=2 x^{3}-9$ : b. Find a f… | Given the function \(y=f(x)=2 x^{3}-9\) |
| None | \[ \begin{aligned} f(2 x)+g(x-1) & =5-2 x+3 x+4 \… | \(f(2x) = 2(2x) - 3 = 4x - 3\) |
| None | If $f(x)=5-9 x$, find $f^{-1}(2)$ Your answer is | The question is asking for the inverse of the function \(f(x) = 5 - 9x\) at the point 2. The invers… |
| None | (a) Find the inverse function of $f(x)=7 x-6$. \[… | The inverse function of a function can be found by swapping the x and y values and solving for y. I… |
| None | The function $f(x)=\frac{12}{x}$ is one-to-one. a… | Let's find the inverse of the function $f(x)=\frac{12}{x}$. To do this, we switch the x and y (or f… |
| None | The following function is one-to-one. Find the in… | The given function is \(f(x)=2x-1\). |
| None | The following function is one-to-one. Find the in… | Let $y = x + 6$. Then $x = y - 6$. |
| None | Find a formula for the inverse of the following f… | The function given is a cubic root function, which is a one-to-one function. This means that it doe… |
| None | Write an expression for the inverse of \[ f(x)=\f… | Given function: \(f(x) = \frac{2}{3}x - 5\) |
| None | For the function $f(x)=4 x+2$, find $f^{-1}(x)$. | Switch the roles of x and y: \(x = 4y + 2\) |