Respuesta :

The inverse of the function [tex]f\left( x \right) = 2x + 3\ is\ {f^{ - 1}}\left( x \right) = \frac{{x - 3}}{2}}[/tex]

Solution:

Given function is:

f(x) = 2x + 3

We have to find the inverse of f(x)

The inverse of a function is writing x  in terms of  y

Let,

y = f(x)

Then,

y = 2x + 3

Exchanges the variables x for y and y for x

[tex]x = 2y + 3[/tex]

Isolate the variable y, which means keep "y" alone in left side of equation

[tex]2y+3 = x\\\\2y = x - 3\\\\y = \frac{x-3}{2}[/tex]

Therefore, inverse of function is:

[tex]f^{-1}(x)= \dfrac{{x - 3}}{2}[/tex]

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