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For f(x) = 2x-3 and g(x)= 2x^2 find,

a) (f + g)(x) = My answer is
2x^2 + 2x - 3. Is this correct?

b) (f - g)(x) How would you do this?

c) (f X g)(2) I do not know what to do since the 2 is there.

Sorry I wanted to add something else!

Determine whether the graph of the following equation is symmetric with respect to the x-axis, the y-axis, and the origin.

y^2 - x - 49 = 0

For x axis -y^2 - x - 9 = 0 is not the same as the first equation so it is not symmetrical to the x-axis. Correct?

For the y-axis y^2 + x - 49 = 0 is not the same as the first equation so it is not symmetrical to the y-axis. Correct?

For the origin -y^2 + x - 49 = 0 is not the same as the first equation so itis not symmetrical to the origin either. Am I correct?

a. (f + g)(x) = f(x) + g(x) =(2x - 3 +
2x^2.

b. (f - g)(x) = f(x) - g(x) = (2x -3)
- 2x^2.

c. (f * g)(x) = f(x) * g(x) = (2x -3)
* 2x^2 = 4x^3 - 6x^2.

y^2 - x - 49 = 0.
Solve for x:
x = y^2 - 49 = 0,
This x parabola is the difference of 2 squares:
(y + 7) (y - 7) = 0,
y + 7 = 0,
y = -7,

y - 7 = 0,
y = 7.

Axis of symmetry: y = (-7+7)/2 = 0,
y = 0 is a hor line which lies on the x axis.

c. (f.g)(2) = f(2) * g(2) = (2*2-3) *
(2 * 2^2) = 1 * 8 = 8.

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