All categories

3 years ago

Composite functions (Question in image)

Mathematics

1 answer:

Annette [7]3 years ago

7 0

$f(0) = - 6 + 4 = - 2 \\ g( - 2) = 4$

You might be interested in

Given = 5-2/3x=1<br> Prove = x=6<br> Proof practice

weeeeeb [17]

Answer:

Plug in x

5 - (2/3*6) = 1

3 0

3 years ago

What are the steps to graphing a linear equation?

chubhunter [2.5K]

Locate the y-intercept on the graph and plot the point.

From this point, use the slope to find a second point and plot it.

Draw the line that connects the two points.

6 0

3 years ago

Read 2 more answers

What is the solution of x - 9/ 7x + 2 < 0

vampirchik [111]

Answer:

x>7

Step-by-step explanation:

6 0

3 years ago

Find the 2nd Derivative:<br> f(x) = 3x⁴ + 2x² - 8x + 4

ad-work [718]

Answer:

$f''(x)=36x^2+4$

Step-by-step explanation:

Let's start by finding the first derivative of $f(x)= 3x^4+2x^2-8x+4$ . We can do so by using the power rule for derivatives.

The power rule states that:

$\frac{d}{dx} (x^n) = n \times x^n^-^1$

This means that if you are taking the derivative of a function with powers, you can bring the power down and multiply it with the coefficient, then reduce the power by 1.

Another rule that we need to note is that the derivative of a constant is 0.

Let's apply the power rule to the function f(x).

$\frac{d}{dx} (3x^4+2x^2-8x+4)$

Bring the exponent down and multiply it with the coefficient. Then, reduce the power by 1.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = ((4)3x^4^-^1+(2)2x^2^-^1-(1)8x^1^-^1+(0)4)$

Simplify the equation.

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x^1-8x^0+0)$
$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8(1)+0)$

$\frac{d}{dx} (3x^4+2x^2-8x+4) = (12x^3+4x-8)$
$f'(x)=12x^3+4x-8$

Now, this is only the first derivative of the function f(x). Let's find the second derivative by applying the power rule once again, but this time to the first derivative, f'(x).

$\frac{d}{d} (f'x) = \frac{d}{dx} (12x^3+4x-8)$

$\frac{d}{dx} (12x^3+4x-8) = ((3)12x^3^-^1 + (1)4x^1^-^1 - (0)8)$

Simplify the equation.

$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4x^0 - 0)$
$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4(1) - 0)$
$\frac{d}{dx} (12x^3+4x-8) = (36x^2 + 4 )$

Therefore, this is the 2nd derivative of the function f(x).

We can say that: $f''(x)=36x^2+4$

6 0

2 years ago

Read 2 more answers

Is the relationship a function? (Show work if possible)

MakcuM [25]

Answer: No! This is not a function!

Step-by-step explanation:

Functions. Terms. Domain - The set of all inputs of a relation or function. Function - A relation in which each input has only one output. Often denoted f (x). Horizontal Line Test - If every horizontal line you can draw passes through only 1 point, x is a function of y.

4 0

4 years ago

Read 2 more answers