All categories

3 years ago

If f(x)=4x+7 and g(x)=x^3, what is (g°f)(-1)

Mathematics

1 answer:

Annette [7]3 years ago

7 0

Answer:

The answer is (g°f)(-1) = 27

Step-by-step explanation:

* (g°f)(1) ⇒ means make the domain of g is the range of f

- At first find the value of f(-1)

- Take the answer and substitute it as the value of x for g

- So the range of f is the domain of g

∵ f(x) = 4x + 7

∵ The domain of f = -1 ⇒ x is the domain

∴ f(-1) = 4(-1) + 7 = -4 + 7 = 3 ⇒ f(-1) is the range

∵ g(x) = x³

∵ x = f(-1) = 3 ⇒ the domain of g

∴ g(3) = 3³ = 27 ⇒ the range of g

* (g°f)(-1) = 27

You might be interested in

What is the area of a rectangle with side lengths of 1/2 and 2/3

ololo11 [35]

Answer:

2/6 square units

Step-by-step explanation:

What is the area of a rectangle with side lengths of 1/2 and 2/3

Step one:

given data

L= 1/2 units

W=2/3 units

Step two:

Area= L*W

substitute

Area= 1/2*2/3

Area=2/6 square units

8 0

2 years ago

Mario is making dinner for 9 people.Mario buys 6 containers of soup.Each container is 18 ounces.If everyone gets the same amount

Triss [41]

The equation for this problem would be
(6*18)/9

6*18 is 108
108/9 is 12
Each person gets 12 oz of soup. This is if they mean mario isnt eating

7 0

3 years ago

Read 2 more answers

WILL GIVE BRAINLIEST find the value of r (-4,8), (r,12), m=4/3 (show your work pls)

OLEGan [10]

Answer:

r = 13

Step-by-step explanation:

The first step is to find b from y=mx=b using m=4/3 and (-4,8)

$8=\frac{4}{3}(-4)+b$

After solving the equation, b will equal -16/3 making the final equation be

$y=\frac{4}{3} x-\frac{16}{3}$

Using the equation, you can solve for r.

$12=\frac{4}{3} x-\frac{16}{3}$

This will bring the answer being r = 13

7 0

2 years ago

Which transformation have been preformed on a graph of f(x)=x2 to obtained the graph of g(x) =-3(x+1)2-4?

avanturin [10]

Horizontal shift because g(x)=f(x+1) 1 unit left

Vertical shift because g(x)=f(x+1)-4 4 units down

Reflected across x-axis because g(x)=-f(x)

Vertically stretched because g(x)=3(f(x))

Step-by-step explanation:

We need to identify which transformation have been preformed on a graph of f(x)=x2 to obtained the graph of g(x) =-3(x+1)2-4?

Rules for transformation:

Horizontal shift: depends on the value h

if g(x)=f(x+h) then: the graph is shifted left h units

if g(x)=f(x-h) then: the graph is shifted right h units

Vertical Shift: depends on the value k

if g(x)=f(x)+k then: the graph is shifted up k units

if g(x)=f(x)-k then: the graph is shifted down k units

Reflection:

if g(x)=-f(x) then graph is reflected at x-axis

if g(x)=f(-x) then graph is reflected at y-axis

Vertical Stretch:

if g(x)=c.f(x) then graph is vertically stretched.

In the given question:

f(x)= x^2

g(x)=-3(x+1)^2-4

Applying the above rules of transformation:

The graph is:

Horizontal shift because g(x)=f(x+1) 1 unit left

Vertical shift because g(x)=f(x+1)-4 4 units down

Reflected across x-axis because g(x)=-f(x)

Vertically stretched because g(x)=3(f(x))

Keywords: Transformations

Learn more about Transformations at:

#learnwithBrainly

7 0

3 years ago

Jake has a rectangular garden that measures 12 feet by 14 feet. He wants to increase the area by 50% and plans to increase each

emmasim [6.3K]

<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

$x\approx 2.9ft$

<h2>Explanation:</h2><h2 />

First of all, let's calculate the area of the original rectangular garden:

$A=b\times h \\ \\ b:base \\ \\ h:height \\ \\ \\ b=12ft \\ \\ h=14ft \\ \\ \\ A=12(14) \\ \\ A=168ft^2$

Jake wants to increase the area by 50%, so the new area would be:

$A'=168(1.5) \\ \\ A'=252ft^2$

He wants to increase the area by 50% and plans to increase each dimension by equal lengths, x, so this is represented by the figure below, therefore:

$(12+x)(14+x)=252 \\ \\ 168+12x+14x+x^2-252=0 \\ \\ x^2+26x-84=0 \\ \\ \\ Using \ quadratic \ formula: \\ \\ x=\frac{-b \pm \sqrt{b^2-4ac}}{2a} \\ \\ a=1 \\ \\ b=26 \\ \\ c=-84 \\ \\ \\ x=\frac{-26 \pm \sqrt{26^2-4(1)(-84)}}{2(1)} \\ \\ x=\frac{-26 \pm \sqrt{1012}}{2} \\ \\ \\ Two \ solutions: \\ \\ x_{1}=-13+\sqrt{253} \approx 2.9\\ \\ x_{2}=-13-\sqrt{253} \approx -28.9 \\ \\ x_{2} \ is \ discarded \ because \ it \ can't \ be \ negatives$

Finally:

<em>In order to increase the area of a rectangular garden that measures 12 feet by 14 feet by 50% Jake must increase each dimension by equal lengths, x:</em>

$x\approx 2.9ft$

<h2>Learn more:</h2>

Dilation: brainly.com/question/10945890

#LearnWithBrainly

6 0

3 years ago