Respuesta :
The inverse of the function [tex]f\left( x \right) = 2x + 3[/tex] is [tex]\boxed{{f^{ - 1}}\left( x \right) = \frac{{x - 3}}{2}}.[/tex]
Further explanation:
A function that is a reverse of another function is known as an inverse function. If we substitute [tex]x[/tex] in a function [tex]f[/tex] and it gives a result of [tex]y[/tex] then its inverse [tex]z[/tex] to [tex]y[/tex] gives the result [tex]x[/tex].
Given:
The given function [tex]f\left( x \right) = 2x + 3[/tex]
Explanation:
Consider [tex]f\left( x \right)[/tex] as [tex]y[/tex].
The function can be expressed as follows,
[tex]y = 2x + 3[/tex]
Solve the above equation to obtain the value of [tex]x[/tex] in terms of [tex]y[/tex].
[tex]\begin{aligned}y&= 2x + 3\\y- 3 &= 2x\\\frac{{y - 3}}{2}&= x\\\end{aligned}[/tex]
Now replace [tex]x[/tex] as [tex]y[/tex].
[tex]y = \dfrac{{x - 3}}{2}[/tex]
Therefore, the inverse of the function is [tex]\dfrac{{x - 3}}{2}.[/tex]
The inverse of the function [tex]f\left( x \right)=2x + 3 \:{\text{is}\: \boxed{{f^{ - 1}}\left( x \right)= \frac{{x - 3}}{2}}.[/tex]
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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.
Inverse of a function f(x)=2x+3 is the opposite of the this function. The inverse of the given function is,
[tex]f^{-1}(x)=\dfrac{x-3}{2}[/tex]
What is inverse of a function?
The inverse of a function is the opposite of the original function. The function and the inverse of it has regularity to each other.
Given information-
The given function is,
[tex]f(x)=2x+3[/tex]
Let the above function is equal to the [tex]y[/tex]. Thus,
[tex]y=f(x)=2x+3[/tex]
Therefore,
[tex]y=2x+3[/tex]
Find the value of variable [tex]x[/tex] in terms of [tex]y[/tex] as,
[tex]y-3=2x\\x=\dfrac{y-3}{2}[/tex]
To get the inverse of the function, interchange the value of the variables [tex]x[/tex] and [tex]y[/tex].
[tex]y=\dfrac{x-3}{2}[/tex]
Hence the inverse of the given function is,
[tex]f^{-1}(x)=\dfrac{x-3}{2}[/tex]
Learn more about the inverse of a function here;
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