Question

Given a function alt="f(x)=3x^4-5x^2+2x-3" align="absmiddle" class="latex-formula">, evaluate $f(-1)$

Answer 1

Answer:

f(-1) = -7

Step-by-step explanation:

f(x) = 3x^4 - 5x^2 +2x -3

Let x = -1

f(-1) = 3 ( -1)^4 - 5(-1)^2 +2(-1) -3

Using the order of operations, do exponents first

f(-1) = 3 ( 1) - 5(1) +2(-1) -3

Then multiply

f(-1) = 3  - 5 -2 -3

Then add and subtract

f(-1) = -7

Answer 2

Answer:

$\huge\boxed{f(-1) = -7}$

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.

$f(-1) = 3(-1)^4 - 5(-1)^2 + 2(-1) - 3$

Now we can solve for the function by multiplying/subtracting/adding our known values.

Starting with the first term to the last term:

• $3(-1)^4 = 3$

WAIT! How is this possible? $-1^4 = -1$ (according to my calculator), and $3 \cdot -1 = -3$, 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 $-2^2$ 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 $-1^4$. However, since we're substituting in -1, it looks like $(-1)^4$, so the expression reads out as "-1 to the fourth."

MULTIPLYING -1 by itself 4 times results in $-1\cdot-1\cdot-1\cdot-1=1$.

Applying this logic to our original term, $3(-1)^4$:

• $3(-1\cdot-1\cdot-1\cdot-1)$
• $3(1)$
• $3$

Therefore, our first term is 3.

Let's move on to our second and third terms.

Second term: $-5x^2$

• $-5(-1)^2$

Applying the same logic from our first term:

• $-5(-1 \cdot -1)$
• $-5(1)$
• $-5$

Third term: $2x$

• $2(-1) = -2$

-3 is just -3, no influence of x.

Combining our terms, we have $3-5-2-3$.

This comes out to be -7, hence, the value of $f(-1)$ for our function $f(x)=3x^4-5x^2+2x-3$ is -7.

Hope this helped!