If the absolute value of x is 4, what is the value of x?
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Answer:
Step-by-step explanation:
In order to solve for this function, we need to substitute in our value of x inside to find f(x). Since we are trying to evalue f(-1), we will substitute -1 in as x to our equation.
Now we can solve for the function by multiplying/subtracting/adding our known values.
Starting with the first term to the last term:
<u><em>WAIT</em></u><em>!</em><em> How is this possible? </em> (according to my calculator), and
, not 3!
It's important to note that taking a power of a negative number and multiplying a negative number are two different things. Let's use as an example.
What your calculator did was follow BEMDAS since it wasn't explicitly told not to.
BEMDAS:
- Brackets
- Exponents
- Multiplication/Division
- Addition/Subtraction
Examining the equation, your calculator used this rule properly. Note that exponents come over multiplication.
So rather than being <em>"-2 squared"</em> - it's <em>"the negative of of 2 squared."</em>
Tying this back into our problem, the squared method would only be true if it looks like . However, since we're substituting in -1, it looks like
, so the expression reads out as "<u><em>-1 to the fourth.</em></u>"
MULTIPLYING -1 by itself 4 times results in .
Applying this logic to our original term, :
Therefore, our first term is 3.
Let's move on to our second and third terms.
Second term:
Applying the same logic from our first term:
Third term:
-3 is just -3, no influence of x.
Combining our terms, we have .
This comes out to be -7, hence, the value of for our function
is <u>-7</u>.
Hope this helped!
The given system of equations in augmented matrix form is
If you need to solve this, first get the matrix in RREF:
- Add 2(row 1) to row 2, row 1 to -3(row 3), and 2(row 1) to 3(row 4):
- Add 11(row 2) to -5(row 3), and 19(row 1) to -5(row 4):
- Add 164(row 3) to -91(row 4):
- Multiply row 4 by 1/13080:
- Add -153(row 4) to row 3:
- Multiply row 3 by -1/91:
- Add 6(row 3) and -8(row 4) to row 2:
- Multiply row 2 by 1/5:
- Add -2(row 2), 4(row 3), and -2(row 4) to row 1:
- Multiply row 1 by 1/3:
So the solution to this system is .