Respuesta :
inverse of f(x) = 2x + 3
y = 2x + 3
so
x = 2y + 3
2y = x - 3
y =1/2x - 3/2
answer
f^-1(x) =1/2x - 3/2
y = 2x + 3
so
x = 2y + 3
2y = x - 3
y =1/2x - 3/2
answer
f^-1(x) =1/2x - 3/2
The inverse of the function is [tex]\boxed{{f^{ - 1}}\left( x \right) = \dfrac{{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 f 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:
Let us assume that [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 is [tex]\boxed{{f^{ - 1}}\left( x \right) = \frac{{x - 3}}{2}}.[/tex]
Learn more:
- Learn more about functions https://brainly.com/question/2142762
- Learn more about range of the functions https://brainly.com/question/3412497
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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.
