The relationship between two numbers is described below, where x represents the first number and y represents the second number.

Hello there!

otez555 [7]

Answer:

24 Domain: s>=2 or s<=-2

25. 3x^2 +14x +10

26. x^2 -2x+5

Step-by-step explanation:

24. Domain is the input or s values

square roots must be greater than or equal to zero

s^2-4 >=0

Add 4 to each side

s^2 >=4

Take the square root

s>=2 or s<=-2

25. f(g(x)) stick g(x) into f(u) every place you see a u

f(u) = 3u^2 +2u-6

g(x) = x+2

f(g(x) = 3(x+2)^2 +2(x+2) -6

Foil the squared term

= 3(x^2 +4x+4) +2x+4-6

Distribute

= 3x^2 +12x+12 +2x+4-6

Combine like terms

=3x^2 +14x +10

26 f(g(x)) stick g(x) into f(u) every place you see a u

f(u) = u^2+4

g(x) = x-1

f(g(x) = (x-1)^2 +4

Foil the squared term

= (x^2 -2x+1) +4

= x^2 -2x+5

7 0

3 years ago

Given:

tekilochka [14]

Quadruple check is so cute and I love it soro much I love it solo much and

3 0

2 years ago

F(x) = x² + 5x-1 is shifted 3 units right. The result is g(x). What is g(x)?

CaHeK987 [17]

Answer:

D

Step-by-step explanation:

When a function is being shifted to the left, all x values will be added by y units shifted. (The constant that comes with x is excluded, eg. 3x shifted by 2 units left, becomes 3(x+2) and not 3x+2.)

Likewise, when a function is being shifted to the right, all x values will be subtracted by y units shifted. (Constant rules applies as well.)

Given f(x) is shifted 3 units right,

the new function, g(x) becomes:

$g(x) = {(x - 3)}^{2} + 5(x - 3) - 1$

Therefore the answer is D in this case.

3 0

1 year ago

Solve for C. Thank you to whoever answers!!!!!!!!!!!!!!!!!!!

faltersainse [42]

Answer:

c=7

Step-by-step explanation:

How to solve your problem

8=−3+29

8=−3c+298=-3c+298=−3c+29

Solve

1

Subtract

29

292929

from both sides of the equation

8=−3+29

8=−3c+298=-3c+298=−3c+29

8−29=−3+29−29

8−29=−3c+29−298{\color{#c92786}{-29}}=-3c+29{\color{#c92786}{-29}}8−29=−3c+29−29

2

Simplify

3

Divide both sides of the equation by the same term

4

Simplify

Solution

=7

Hope this helps!

Have a great day!

-Lea

5 0

2 years ago

Read 2 more answers

Verify that the function <img src="https://tex.z-dn.net/?f=g%28x%29%3D2x%5E3-3x%2B1" id="TexFormula1" title="g(x)=2x^3-3x+1" alt

ch4aika [34]

Lets check if the three conditions hold.

1 : Continuity of g on the interval [0,2]

First, g(x) is a continuous function on R, as the sum of a cubic function wich is continuous on R, and a linear polynomial of the form ax + b which is also continuous on R. Finally g is also continuous on the interval [0,2]

2 : Differentiable on the same interval

Since the cubic function and the linear polynomial one are differentiable on R, g also is differentiable and particularly on the interval [0,2]

Also we have g'(x) = 2*3*x² - 3 = 6x² - 3

3 : Do we have g(0) = g(2) ?

Lets compute g(0) = 2*0^3 - 3*0 + 1 = 1

And g(2) = 2*2^3 - 3*2 + 1 = 2 * 8 - 6 + 1 = 16 - 6 + 1 = 11

Since g(0) ≠ g(2), Rolle's theorem is not applicable. Thus unfortunately, we can not conclude that there exist c ∈ (0,2) such that f'(c) = 0

5 0

2 years ago