Okay i have a few function questions im gonna post. Im completely confused with these so any help would be great.
Minimum or maximum value of:
f(x)=2x^2+4x+1
and
f(x)=x^2-3x+2
then
if f(x)=x^2+9 and g(x)=x-4,
find (g*f)(-3)
next is
if f(x)=x^3+x^2-x-1 and g(x)=x+1,
find (f/g)(n)
and the possible solutions to the problem are
A) n^2-x-1
B) (n^2+x-1/n+1)
C) n+1
D) n^2-1
and last, find the zeroes of
f(x)=2x^2-10
thanks for any help!
<< find the zeroes of
f(x)= 2x^2-10 >>
f(x) = 2(x^2 -5)
= 2(x + sqrt 5)(x - sqrt 5)
When either of the x-containing factors is zero, f(x) is zero.
<<Minimum or maximum value of:
f(x)=2x^2+4x+1
and .. >>
Since you aren't taking calculus and presumably do not know about deriviatives, I suggest you use the method of "completing the square"
f(x)= 2(x^2 + 2x) + 1
= 2 (x^2 + 2x + 1) -1
= 2(x+1)^2 -1
It should be evident that this will be have a minimum when x+1 = 0. That tells you what x is there.
Sure! I'll guide you through solving these function questions step by step.
1. Finding the minimum or maximum value of a function:
To find the minimum or maximum value of a function, we need to determine the vertex of the parabola represented by the function.
For the function f(x) = 2x^2 + 4x + 1:
a. Identify the quadratic term coefficient (a) as 2.
b. The vertex of a quadratic function is given by (-b/2a, f(-b/2a)).
c. Calculate the x-coordinate using the formula: -b/2a. In this case, it is -4/(2*2) = -4/4 = -1.
d. Substitute the x-coordinate into the function: f(-1) = 2(-1)^2 + 4(-1) + 1 = 2 - 4 + 1 = -1.
So, the minimum value of f(x) = 2x^2 + 4x + 1 is -1, and it occurs at x = -1.
For the function f(x) = x^2 - 3x + 2:
a. Identify the quadratic term coefficient (a) as 1.
b. Calculate the x-coordinate of the vertex using the formula: -b/2a. In this case, it is 3/(2*1) = 3/2.
c. Substitute the x-coordinate into the function: f(3/2) = (3/2)^2 - 3(3/2) + 2 = 9/4 - 9/2 + 2 = 1/4.
So, the minimum value of f(x) = x^2 - 3x + 2 is 1/4, and it occurs at x = 3/2.
2. Evaluating composite functions:
To evaluate the composite function (g*f)(-3), we need to compute g(-3) and then substitute it into the function f(x).
For g(x) = x - 4:
a. g(-3) = -3 - 4 = -7.
Now, we substitute g(-3) into the function f(x) = x^2 + 9:
b. f(-7) = (-7)^2 + 9 = 49 + 9 = 58.
So, (g*f)(-3) = 58.
3. Evaluating division of functions:
To find the value of (f/g)(n), we divide f(n) by g(n).
For f(x) = x^3 + x^2 - x - 1 and g(x) = x + 1:
a. Substitute n into f(x): f(n) = n^3 + n^2 - n - 1.
b. Substitute n into g(x): g(n) = n + 1.
c. Divide f(n) by g(n): (f/g)(n) = (n^3 + n^2 - n - 1) / (n + 1).
4. Finding the zeros of a function:
To find the zeroes of f(x) = 2x^2 - 10, we set f(x) equal to 0 and solve for x.
a. Set f(x) = 2x^2 - 10 equal to 0: 2x^2 - 10 = 0.
b. Add 10 to both sides: 2x^2 = 10.
c. Divide both sides by 2: x^2 = 5.
d. Take the square root of both sides: x = ±√5.
So, the zeroes of f(x) = 2x^2 - 10 are x = √5 and x = -√5.
I hope this helps! Let me know if you have any further questions.