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What is the inverse of the function f(x)=-\dfrac{1}{2}(x+3)f(x)=− 2 1 ​ (x+3)f, left parenthesis, x, right parenthesis, equals, minus, start fraction, 1, divided by, 2, end fraction, left parenthesis, x, plus, 3, right parenthesis

Respuesta :

Acarico

Answer:

The inverse of the function is

-2x-3

Step-by-step explanation:

ajeigbeibraheem

The inverse of the function f(x) = -\dfrac{1}{2}(x+3) is f(x)⁻¹ = -2x - 3

What is the inverse of a function?

The inverse of a function is a function that gives us the actual value for which the desired function has a given result.

The given function is:

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

To find the inverse, we need to follow the following steps

  • replace the role of f(x) by y;

[tex]\mathbf{ y=-\dfrac{(x+3)}{2}}[/tex]

  • Swap x and y variables

[tex]\mathbf{ x=-\dfrac{(y+3)}{2}}[/tex]

  • Solve for y;

2x = - (y + 3)

2x = -y - 3

y = -2x - 3

Writing back in inverse notation, we have:

f(x)⁻¹ = -2x - 3

Learn more about the inverse of a function here:

https://brainly.com/question/2873333

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