Question

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Q. 13
What is the inverse of the function f (x) = 3(x + 2)2 – 5, such that x ≤ –2?

A. inverse of f of x is equal to negative 2 plus the square root of the quantity x over 3 plus 5 end quantity
B. inverse of f of x is equal to negative 2 minus the square root of the quantity x over 3 plus 5 end quantity
C. inverse of f of x is equal to negative 2 minus the square root of the quantity x plus 5 all over 3 end quantity
D. inverse of f of x is equal to negative 2 plus the square root of the quantity x plus 5 all over 3 end quantity

Answer 1

Explanation:

The correct answer is A.

The inverse of a function is the function that reverses the output and input of the original function. In other words, if f(x) = y, then the inverse of f(x) is y = f^(-1)(x).

To find the inverse of f(x), we start by replacing f(x) with y. This gives us the equation y = 3(x + 2)2 – 5. We then solve for x in terms of y.

First, we add 5 to both sides of the equation. This gives us y + 5 = 3(x + 2)2.

Then, we divide both sides of the equation by 3. This gives us (y + 5)/3 = (x + 2)2.

We take the square root of both sides of the equation. This gives us sqrt[(y + 5)/3] = x + 2.

Finally, we subtract 2 from both sides of the equation. This gives us sqrt[(y + 5)/3] - 2 = x.