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.
a) To find (f + g)(x), you need to add the functions f(x) and g(x).
Given f(x) = 2x - 3 and g(x) = 2x^2, we can combine them by adding their respective terms. So,
(f + g)(x) = f(x) + g(x)
= (2x - 3) + (2x^2)
Simplifying by combining like terms, we get:
(f + g)(x) = 2x^2 + 2x - 3
Your answer, 2x^2 + 2x - 3, is indeed correct.
b) To find (f - g)(x), you need to subtract the function g(x) from f(x).
Using the same functions f(x) = 2x - 3 and g(x) = 2x^2, we can subtract g(x) from f(x) by changing the sign of every term in g(x) and then combining the terms:
(f - g)(x) = f(x) - g(x)
= (2x - 3) - (2x^2)
Simplifying by combining like terms, we get:
(f - g)(x) = 2x - 2x^2 - 3
So, (f - g)(x) = 2x - 2x^2 - 3.
c) To evaluate (f x g)(2), you need to multiply the two functions f(x) and g(x) and substitute x with 2.
Given f(x) = 2x - 3 and g(x) = 2x^2, we can multiply them by substituting x with 2:
(f x g)(2) = f(2) * g(2)
= (2 * 2 - 3) * (2^2)
Simplifying further, we get:
(f x g)(2) = (4 - 3) * 4
= 1 * 4
= 4
Therefore, (f x g)(2) equals 4.