Question

Which function is the inverse of f(x)=2x+3

Answer 1

Answer:

$f^{-1}(x)=\frac{x-3}{2}$

Step-by-step explanation:

we have

$f(x)=2x+3$

Let

$y=f(x)$

$y=2x+3$

Exchanges the variables x for y and y for x

$x=2y+3$

Isolate the variable y

$2y=x-3$

$y=\frac{x-3}{2}$

Let

$f^{-1}(x)=y$

$f^{-1}(x)=\frac{x-3}{2}$

Answer 2

The inverse of the function $f\left( x \right) = 2x + 3$ is $\boxed{{f^{ - 1}}\left( x \right) = \frac{{x - 3}}{2}}.$

Further explanation:

A function that is a reverse of another function is known as an inverse function. If we substitute $x$ in a function $f$ and it gives a result of $y$ then its inverse $z$ to $y$ gives the result $x$.

Given:

The given function $f\left( x \right) = 2x + 3$

Explanation:

Consider $f\left( x \right)$ as $y$.

The function can be expressed as follows,

$y = 2x + 3$

Solve the above equation to obtain the value of $x$ in terms of $y$.

$\begin{aligned}y&= 2x + 3\\y- 3 &= 2x\\\frac{{y - 3}}{2}&= x\\\end{aligned}$

Now replace $x$ as $y$.

$y = \dfrac{{x - 3}}{2}$

Therefore, the inverse of the function is $\dfrac{{x - 3}}{2}.$

The inverse of the function $f\left( x \right)=2x + 3 \:{\text{is}\: \boxed{{f^{ - 1}}\left( x \right)= \frac{{x - 3}}{2}}.$

Learn more:

1. Learn more about functions brainly.com/question/2142762
2. Learn more about range of the functions brainly.com/question/3412497
3. Learn more about relation and function brainly.com/question/1691598

Answer details:

Grade: High school

Subject: Mathematics

Chapter: Functions

Keywords: functions, range, domain, inverse, reverse, fraction, relation, expression, inverse of the function, one-one, onto, invertible.