Again with another math problem?

Question

this is totally confusing. I dont know what they want. The problem is For the function f(x) = x with a power of two - 2x + 1
(a) find f(0)

(b) solve f(x) = 0

Can anyone help me with this one?

Answer 1

nope sorry

Answer 2

(a) f(x) = x^2 - 2x +1, so that f(0) = 0 - 0 + 1 = + 1.

(b) f(x) = x^2 - 2x +1 = (x - 1)^2.

So, if f(x) = 0, (x - 1)^2 = 0. This means that there is a REPEATED or DOUBLE root, x = 1.

[We say "repeated" because the expectation is that a quadratic equation will in general have two roots, whether real or complex. It often helps to VISUALIZE what kind of curve a function y = f(x) will be. Graphically, a general quadratic expression like this particular f(x) is either an upward-opening or a downward-opening parabola. (This one in fact opens upwards.) Its real roots (if any) are where the parabola crosses the x-axis. IF, HOWEVER, the parabola TOUCHES the x-axis, we can regard it as the limit of two real roots coming together, as the parabola as a whole moves upwards or downwards. Hence a "repeated" or "double" root.]

Live long and prosper.

Answer 3

f(0) is when you plug in 0 for x (if it had been f(2), you would have had to plug in 2 for x). So it is 0 square -2*0+1=1. So f(0) is 1.

The next part is trickier. f(x)=0 is the same as xsquared-2x+1=0. therefore 0=(x-1)(x-1). again 0=(x-1)^2. so x=1 when f(x)=0. This is called a root of the function.

Answer 4

OK, first you need to understand functions. f(x) or g(x) or anyletterofthealphabet(x) means the function depends on the variable x, or whatever happens to be in the brackets. In other words, for a given value of x, (or whatever variable is used), another certain number (or more) is given out. You can always google "functions" and get far better explanations.

So for (a):
f(0) means substitute ('put') zero as the value of 'x'. So everywhere you see 'x' substitute the value zero. This gives

0^(-2x0 + 1)

that ^ means 'with a power of'. Now, zero raised to any number is zero, because no matter how many times you multiply zero with itself, it remains zero!

For (b):
this means put the whole thingy f(x) is equal to, equal to zero, in this example this means:
x^(-2x+1)=0
Now, the only way a number (that is, 'x' in this case) when raised to a power, can equal zero, is when the base ( the number which is being raised to a power- the number at the bottom), is when the base is zero. Think about it, to what power must 5 be raised to gt zero? Or 4? Or 2383244837? Or 0.00000002352?
Only zero raised to a power can equal zero, therefore:

x=0.

Answer 5

a) Just plug in 0 for x.
0^2 - 2(0) + 1 = 1

b) Make the equation =0
x^2 - 2x + 1 = 0
Now factor.
(x-1) (x-1) = 0
solve each binomial by making them =0. Since they're the same, you only have to do it once. so f(x)=0 when x=1

Answer 6

area = length * width or 112 = L*W length is 6 better than width interprets to L= W+6 then you definately replace each and each variable. If L = W+6, then we can replace in W+6 for the L in L*W. Therefor, W*(W+6) = 112. W^2 + 6W =112. subtract 112 from the two facets. W^2 + 6W - 112 = 0 Then ingredient the equation. (W+14)(W-8) = 0 you may then clean up for W by utilising splitting the two binomials. W+14 = 0. W-8=0 subtract 14 W = -14 upload 8 W = 8 so we've 2 values for W, yet wait, how can the width be damaging??? it won't be able to, so W could be 8cm. We could then bypass lower back to the two certainly one of our unique equations. L = W+6, and replace in 8 for W. L = (8) +6 8+6 = 14 L = 14cm, and W = 8cm

Answer 7

x with a power of two is commonly notated like this:
x^2... (that's how you put it into a graphing calculator...

f(x)=x^2 - 2x +1

So when it's f(0), you plug 0 in for all of the x's in the equation... same for f(1) or f(y)

So f(0)=(0)^2 - 2(0) + 1
0^2=0, so 0- 2*0 which is also 0
0-0+1=1
f(0)=1

When f(x)=0, you put 0 in the place of f(x)
0=x^2-2x+1
So you have to factor this...
(x+2)(x-1)
0=(x+2)(x-1)
One of these two factors have to equal zero for this equation to work, because anything times zero equals zero

so x+2 has to equal zero.. for it to equal zero
x+2=0, you subtract 2 from both sides and you get
x=-2... because (-2)+2=0
Do the same thing for x-1=0
Add one to both sides, then you get x=1
because(1)-1=0

So your answer for f(x)=0 is x=-2 and x=1

Answer 8

f(x) = x^2 - 2x + 1

a. f(0) just means put x=0 into the equation and calculate
f(0) = 0^2 - 2(0) + 1 = 1

b. f(x) = 0 = x^2 - 2x + 1 = (x - 1)(x - 1) and x = 1

Answer 9

f(x) = x^2 - 2x + 1
To find f(0), substitute 0 for x
f(x) = 0^2 - 2*0 + 1 = 1
To solve f(x) = 0
x^2 - 2x + 1 = 0
(x - 1)^2 = 0
x = 1

Answer 10

f(x) = x^2 - 2x + 1
Use quadratic formula: (ax^2 + bx + c)
f(x) = 0 when x = [-b +- Sq Rt (b^2 - 4ac)]/2a
[2 +- Sq Rt(4 - 4)]/2
(2 +- 0)/2
x = 1

you can also solve by factoring

x^2 - 2x + 1 = (x-1) (x-1)
x = 1

Answer 11

a) f(0) --- f(x)=x^2-2x+1=0^2-2(0)+1=1
so f(x)=1

b) factor 0=x^2-2x+1 --- (x-1)(x-1) = (x-1)^2