David performed the following mathematical operation .

C:  x = 1/2

Step-by-step explanation:

Set the divisor, 2x - 1, equal to zero and solve for x:  2x = 1, so x = 1/2.  Statement C is true.

The correct option is C.

Step-by-step explanation:

If a function f(x) is completely divisible by (x-a), it means (x-a) is a factor of f(x) and x=a is a root of that polynomial.

The given polynomial is

It is given that when David divide the above polynomial by (2x-1), then he get

Since the remainder is zero it means P(x) is completely divisible by (2x-1) or (2x-1) is a factor of P(x).

Add 1 on both the sides.

Divide both sides by 2.

It means must be a root of the polynomial .

Therefore, the correct option is C.

g(x) = x² + 2

step-by-step explanation:

it is given that the graphs are the same shape.

the only difference is that the red graph is 2 units higher than the blue graph.

that is to say that the red graph is simply the blue graph that has been moved vertically by 2 units in the positive y direction.

hence

g(x) = f(x) + 2

or

g(x) = x² + 2