Question

Given that f(x) = x^2 - 3 all over 2 Find f(3) Find f^-1(x) Find f^-1(11)

Answer 1

Explanation:

f(3) = (3^2 - 3) / 2

= 6/2

= 3.

Let f(x) = y then

y = (x^2 - 3)/2

2y = x^2 - 3

x^2 = 2y + 3

x = √(2y +3)

So

f^-1(x) = √(2x + 3)

f^-1(11) = √(2(11) + 3)

= √25

= 5.

Answer 2

Answer: Therefore, f(3) is equal to 3. Therefore, f^-1(11) is equal to 5.

Explanation:

1. To find f(3), substitute x = 3 into the function f(x) = x^2 - 3/2:

f(3) = (3^2 - 3)/2

= (9 - 3)/2

= 6/2

= 3

2. To find the inverse function f^-1(x), we need to swap the roles of x and y in the original equation and solve for y. Let's do that:

x = (y^2 - 3)/2

Now, let's solve for y:

Multiply both sides by 2:

2x = y^2 - 3

Add 3 to both sides:

2x + 3 = y^2

Take the square root of both sides:

√(2x + 3) = y

Therefore, the inverse function f^-1(x) is equal to √(2x + 3).

3. To find f^-1(11), substitute x = 11 into the inverse function √(2x + 3):

f^-1(11) = √(2(11) + 3)

= √(22 + 3)

= √25

= 5