Question

F(x) = x2. What is g(x)?

Answer 1

The Domain of g (x) = x2 is all the Real Numbers.

Step-by-step explanation:

The composed function is: (g º f) (x) = g (f (x)) = (√x)2. = x. Now, "x" normally has the Domain of all Real Numbers ... ... but because it is a composed function we must also consider f (x), So the Domain is all non-negative Real Numbers.

Answer 2

The value of g(x) = (4x)².

Given the point (1, 16) and the function f(x) = x², we can find the value of g(x) such that g(1) = 16.

Since we don't have the explicit form of g(x), we can use the given point (1, 16) to find its value. We can substitute x = 1 into the function f(x) to find the value of g(1):

g(1) = f(1) = (1)² = 1

Now, we can use the point (1, 1) and the function f(x) = x^2 to find the value of g(x) such that g(1) = 16. We can rewrite the equation as:

16 = (x²)

To solve for x, we can take the square root of both sides of the equation:

x² = 16 => x = ±4

Since x cannot be negative, we choose x = 4. Therefore, the point (4, 16) lies on the parabola y = x².

Now, we can find the value of g(x) at x = 4:

g(4) = f(4) = (4)² = 16

Since g(4) = 16 and g(1) = 1, we can conclude that g(x) = (4x)². This is option D.