Question

How do you find the inverse of $y = 4x + 7?$

Answer 1

As per the given question we have to find the inverse of the given function. We can say that inverse in terms of mathematical language refers to the opposite of another operation. It is used in various mathematical terms and almost used in all new topics. Basically an inverse function undoes the original function by switching the input and output. If there is a function $y = f(x)$, then the inverse function would be $x = {f^{ - 1}}(y)$.

Complete step by step answer:
Here we have the given function $y = 4x + 7$. We usually have a function expressed as $y = f(x)$. In this question to find the inverse function we need to isolate the $x$ variable and then express it as dependent on the $y$ variable.
By transferring the constant term to the left hand side we have: $y - 7 = 4x$.
Now by isolating the x- variable: $x = \dfrac{{y - 7}}{4}$.
Hence the required answer is $x = \dfrac{{y - 7}}{4}$.

Note: We should note that reciprocal and inverse are two terms. A reciprocal can be an inverse but an inverse cannot be a reciprocal . A reciprocal is a multiplicative inverse. Also we can represent a reciprocal in different ways but it does not have any specific sign whereas an inverse is represented as ${f^{ - 1}}(x)$. We can say that an inverse function is also known as anti-function which is defined as the function which can reverse into another function that means if the function accepts a certain value or performs the particular operation on the values and generates an output then the inverse function agrees the result.