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?
a) To find (f + g)(x), you need to add the two functions f(x) and g(x) together.
f(x) = 2x - 3
g(x) = 2x^2
To add these two functions, you add up the corresponding terms:
(f + g)(x) = (2x - 3) + (2x^2)
Simplifying the expression, you get:
(f + g)(x) = 2x^2 + 2x - 3
So your answer of 2x^2 + 2x - 3 is correct.
b) To find (f - g)(x), you need to subtract the two functions f(x) and g(x) from each other.
(f - g)(x) = (2x - 3) - (2x^2)
Simplifying the expression, you get:
(f - g)(x) = -2x^2 + 2x - 3
c) To evaluate (f x g)(2), you need to substitute x = 2 into the expression f(x) * g(x).
f(x) = 2x - 3
g(x) = 2x^2
(f x g)(x) = (2x - 3) * (2x^2)
Substituting x = 2:
(f x g)(2) = (2 * 2 - 3) * (2 * 2^2)
= (4 - 3) * (8)
= 1 * 8
= 8
So the value of (f x g)(2) is 8.
Regarding the graph:
For the x-axis, your observation is correct. The equation y^2 - x - 49 = 0 does not remain the same when you substitute -y for y. Therefore, it is not symmetric with respect to the x-axis.
For the y-axis, your observation is also correct. The equation y^2 + x - 49 = 0 does not remain the same when you substitute -x for x. Therefore, it is not symmetric with respect to the y-axis.
For the origin, your observation is correct again. The equation -y^2 + x - 49 = 0 does not remain the same when you substitute -x for x and -y for y. Therefore, it is not symmetric with respect to the origin.