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.
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?
Nevermind,I did not realize that my question was already answered.
b) the same way you did a) , except ..
2x - 3 - (2x^2) =
(f-g)(x) = - 2x^2+ 2x - 3
c) in this case you multiply,
(fxg)(x) = (2x-3)(2x^2
then fxg(2) = (4-3)(8) = .... (I just replaced the x with 2)
a) To find (f + g)(x), you need to add the functions f(x) and g(x) together.
So, (f + g)(x) = f(x) + g(x) = (2x - 3) + (2x^2)
Simplifying this expression, we get:
(f + g)(x) = 2x^2 + 2x - 3
Your answer of 2x^2 + 2x - 3 is correct.
b) To find (f - g)(x), you need to subtract the function g(x) from f(x).
So, (f - g)(x) = f(x) - g(x) = (2x - 3) - (2x^2)
Simplifying this expression, we get:
(f - g)(x) = -2x^2 + 2x - 3
c) To evaluate (f * g)(2), you need to substitute x = 2 into the expression for (f * g)(x).
So, (f * g)(2) = f(2) * g(2) = (2(2) - 3) * (2(2)^2)
Simplifying this expression, we get:
(f * g)(2) = (4 - 3) * (2 * 4) = 1 * 8 = 8
Therefore, (f * g)(2) = 8.
Regarding the question about symmetry:
For the x-axis:
You correctly determined that the equation -y^2 - x - 9 = 0 is not the same as the given equation y^2 - x - 49 = 0. Therefore, the graph is not symmetric with respect to the x-axis.
For the y-axis:
You correctly determined that the equation y^2 + x - 49 = 0 is not the same as the given equation y^2 - x - 49 = 0. Therefore, the graph is not symmetric with respect to the y-axis.
For the origin:
You correctly determined that the equation -y^2 + x - 49 = 0 is not the same as the given equation y^2 - x - 49 = 0. Therefore, the graph is not symmetric with respect to the origin.
You are correct in all your conclusions.