Question

What is inverse equations and a example?

Answer 1

A function that consists of its invrse fetches the original value
f(y) = 2y + 3, and its inverse function is f-1(y) = (y - 3)/2.

Answer 2

An inverse function, in simple terms, is a function that serves to *undo* another function by switching the positions of 'x' and 'y'

An inverse function is denoted as \(\large f^{-1}(x) \)

An example would be as follow, say you have: \(y = 2x-10 \)

To find the inverse, switch the variables and solve:
\(\color{red}{y}=2\color{gold}{x}-10 \) becomes this: \(\color{gold}{x}=2\color{red}{y}-10 \)

Now just solve for \(\color{red}{y}\) again:
\[\large \color{gold}{x}(+10)=2\color{red}{y}-10(+10) \]
Divide by 2:
\[\large \frac{\color{gold}{x} +10}{2} = \frac{2\color{red}{y}}{2} \]
And then you get the inverse equation:
\[\large \frac{\color{gold}{x}}{2} +5 = \color{red}{y} \]

Denoted as an inverse function:
\[\large \color{red}{f^{-1}(x)} = \frac{\color{gold}{x}}{2} +5 \]

Answer 3

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Answer 4

mm

Answer 5

hmmm

Answer 6

Inverse equations involve operations that "undo" each other. For example, the inverse of addition is subtraction, and the inverse of multiplication is division. One example of an inverse equation is:

Original equation: 2x + 3 = 11
Inverse operation: 2x = 11 - 3
Solving for x: x = (11 - 3) / 2
Answer: x = 4