Answer:
[tex]\huge\boxed{f(-1) = -7}[/tex]
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.
[tex]f(-1) = 3(-1)^4 - 5(-1)^2 + 2(-1) - 3[/tex]
Now we can solve for the function by multiplying/subtracting/adding our known values.
Starting with the first term to the last term:
WAIT! How is this possible? [tex]-1^4 = -1[/tex] (according to my calculator), and [tex]3 \cdot -1 = -3[/tex], 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 [tex]-2^2[/tex] 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 "-2 squared" - it's "the negative of of 2 squared."
Tying this back into our problem, the squared method would only be true if it looks like [tex]-1^4[/tex]. However, since we're substituting in -1, it looks like [tex](-1)^4[/tex], so the expression reads out as "-1 to the fourth."
MULTIPLYING -1 by itself 4 times results in [tex]-1\cdot-1\cdot-1\cdot-1=1[/tex].
Applying this logic to our original term, [tex]3(-1)^4[/tex]:
- [tex]3(-1\cdot-1\cdot-1\cdot-1)[/tex]
- [tex]3(1)[/tex]
- [tex]3[/tex]
Therefore, our first term is 3.
Let's move on to our second and third terms.
Second term: [tex]-5x^2[/tex]
Applying the same logic from our first term:
- [tex]-5(-1 \cdot -1)[/tex]
- [tex]-5(1)[/tex]
- [tex]-5[/tex]
Third term: [tex]2x[/tex]
-3 is just -3, no influence of x.
Combining our terms, we have [tex]3-5-2-3[/tex].
This comes out to be -7, hence, the value of [tex]f(-1)[/tex] for our function [tex]f(x)=3x^4-5x^2+2x-3[/tex] is -7.
Hope this helped!
