All categories

2 years ago

Let f(x) = 3x² + 1 and g(x) = x +4. Find (f +g)(x) and (f -g)(x).

Mathematics

1 answer:

Artist 52 [7]2 years ago

6 0

Answer:

(f + g)(x) = 3x² + x + 5

(f - g)(x) = 3x² - x - 3

Step-by-step explanation:

(f + g)(x) → f(x) + g(x) → 3x² + 1 + x + 4

Combine like terms and you get: 3x² + x + 5

(f - g)(x) → f(x) - g(x) → 3x² + 1 - (x + 4)

Remember to distribute the neg. everything in the parentheses. Combine like terms and you get: 3x² - x - 3

You might be interested in

There are 336days in leap year and 24 hours in a day how many hours are in leap year?

valentina_108 [34]

Answer:

One leap year contains 8784 hours. Hope this helps. :)

7 0

3 years ago

<img src="https://tex.z-dn.net/?f=%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx%20%5Csqrt%7Bx....%7D%20%7D%20%7D%20%7D%20%20%3D%20%

andrey2020 [161]

First observe that if $a+b>0$ ,

$(a + b)^2 = a^2 + 2ab + b^2 \\\\ \implies a + b = \sqrt{a^2 + 2ab + b^2} = \sqrt{a^2 + ab + b(a + b)} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b(a+b)}}} \\\\ \implies a + b = \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{a^2 + ab + b \sqrt{\cdots}}}}$

Let $a=0$ and $b=x$ . It follows that

$a+b = x = \sqrt{x \sqrt{x \sqrt{x \sqrt{\cdots}}}}$

Now let $b=1$ , so $a^2+a=4x$ . Solving for $a$ ,

$a^2 + a - 4x = 0 \implies a = \dfrac{-1 + \sqrt{1+16x}}2$

which means

$a+b = \dfrac{1 + \sqrt{1+16x}}2 = \sqrt{4x + \sqrt{4x + \sqrt{4x + \sqrt{\cdots}}}}$

Now solve for $x$ .

$x = \dfrac{1 + \sqrt{1 + 16x}}2 \\\\ 2x = 1 + \sqrt{1 + 16x} \\\\ 2x - 1 = \sqrt{1 + 16x} \\\\ (2x-1)^2 = \left(\sqrt{1 + 16x}\right)^2$

(note that we assume $2x-1\ge0$ )

$4x^2 - 4x + 1 = 1 + 16x \\\\ 4x^2 - 20x = 0 \\\\ 4x (x - 5) = 0 \\\\ 4x = 0 \text{ or } x - 5 = 0 \\\\ \implies x = 0 \text{ or } \boxed{x = 5}$

(we omit $x=0$ since $2\cdot0-1=-1\ge0$ is not true)

3 0

1 year ago

Solve: 2 + 2x=19 + 2x 2=19 Answer: No Solutions

riadik2000 [5.3K]

Answer:

no solution

Step-by-step explanation:

2+2x=19+2x

2x-2x=19-2

0=17

6 0

2 years ago

This is dueeeeeee tomorow please help

xxMikexx [17]

Answer:

What’s the question?

Step-by-step explanation:

3 0

2 years ago

Identify the factors of the terms of the expression 5+6a+11b

emmainna [20.7K]

Letters used to represent values or unknown quantities that can change or vary. One example of an algebraic expression is 3x – 4. Notice the variable,

3 0

3 years ago