Respuesta :

Answer:

B; 1

Step-by-step explanation:

Firstly, we need to find the inverse of the given function

Let us have f(x) as y

To find the inverse, we set out to make x the formula subject

Thus;

y = √(3x + 6)

square both sides

y^2 = 3x + 6

3x = y^2 - 6

x = (y^2 - 6)/3

To write the inverse, replace y by x

So we have the inverse of the function as ;

(x^2 - 6)/3

So what we have to do here is to substitute 3 for x in the inverse

We have this as;

(3^2 -6)/3

(9-6)/3

= 3/3 = 1

VirαtKσhli

Answer:

1 ( option B )

Step-by-step explanation:

The given equation is ,

[tex]\implies f(x) =\sqrt{ 3x + 6 }[/tex]

Now substituting y = f(x) , we have ,

[tex]\implies y=\sqrt{ 3x + 6 }[/tex]

For finding the inverse , Interchange x and y , we have ,

[tex]\implies x =\sqrt{ 3y + 6 }[/tex]

Now solve for y , we have ,

[tex]\implies x ^2=3y + 6 \\\\\implies 3y = x^2-6 \\\\\implies y =\dfrac{x^2-6}{3} [/tex]

Now replace y with f-¹(x) , we have ,

[tex]\implies f^{-1}(x) =\dfrac{x^2-6}{3} [/tex]

Now put x = 3 , we have ,

[tex]\implies f^{-1}(3) =\dfrac{3^2-6}{3}\\\\\implies f^{-1}(3) = \dfrac{9-6}{3}\\\\\implies \underline{\underline{ f^{-1}(3) = 1 }} [/tex]

Otras preguntas