Question

50 POINTS FOR THIS MATH QUESTION

Answer 1

1 ( option B )

Explanation:

The given equation is ,

`\implies f(x) =√( 3x + 6 )`

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

`\implies y=√( 3x + 6 )`

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

`\implies x =√( 3y + 6 )`

Now solve for y , we have ,

`\implies x ^2=3y + 6 \\\\\implies 3y = x^2-6 \\\\\implies y =(x^2-6)/(3)`

Now replace y with f-¹(x) , we have ,

`\implies f^(-1)(x) =(x^2-6)/(3)`

Now put x = 3 , we have ,

`\implies f^(-1)(3) =(3^2-6)/(3)\\\\\implies f^(-1)(3) = (9-6)/(3)\\\\\implies \underline{\underline{ f^(-1)(3) = 1 }}`

Answer 2

B; 1

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