Finding the Inverse

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.

The problems about Finding the Inverse

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 \…	$f (2 x) = 2 (2 x) - 3 = 4 x - 3$
None	If $f (x) = 5 - 9 x$ , find $f^{- 1} (2)$ Your answer is	The question is asking for the inverse of the function $f (x) = 5 - 9 x$ 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 $f (x) = 2 x - 1$ .
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: $x = 4 y + 2$