1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Free_Kalibri [48]
4 years ago
15

Let $f(x) = 2x^2 + 3x - 9,$ $g(x) = 5x + 11,$ and $h(x) = -3x^2 + 1.$ Find $f(x) - g(x) + h(x).$

Mathematics
1 answer:
Viefleur [7K]4 years ago
6 0

QUESTION 1

Given that:

f(x)=2x^2+3x-9,

g(x)=5x+11,

and

h(x)=-3x^2+1

Then;

f(x)-g(x)+h(x)=2x^2+3x-9-(5x+11)+(-3x^2+1)

f(x)-g(x)+h(x)=2x^2+3x-9-5x-11-3x^2+1

Group similar terms;

f(x)-g(x)+h(x)=2x^2-3x^2+3x-5x-11-9+1

Simplify;

f(x)-g(x)+h(x)=-x^2-2x-19

QUESTION 2

Given that;

f(x)=4x-7.

g(x)=(x+1)^2

and

s(x)=f(x)+g(x)

Substitute the functions;

s(x)=4x-7+(x+1)^2

Substitute x=3

s(3)=4(3)-7+(3+1)^2

s(3)=12-7+(4)^2

s(3)=5+16

s(3)=21

QUESTION 3

Given:

f(x)=3x+2

g(x)=x^2-5x-1

f(g(x))=f(x^2-5x-1)

This implies that;

f(g(x))=3(x^2-5x-1)+2

Expand the parenthesis;

f(g(x))=3x^2-15x-3+2

f(g(x))=3x^2-15x-1

QUESTION 4

The given function is;

f(x)=3(x-6)^2+1

Let

y=3(x-6)^2+1

\Rightarrow y-1=3(x-6)^2

\Rightarrow \frac{y-1}{3}=(x-6)^2

\Rightarrow \sqrt{\frac{y-1}{3}}=x-6

\Rightarrow x=6+\sqrt{\frac{y-1}{3}}

The range is:

\frac{y-1}{3}\ge0

y-1\ge0

y\ge1

The interval notation is;

[1,+\infty)

You might be interested in
Write f(x) = 2x2 – 44x + 185 in vertex form.
forsale [732]

Answer:

Step-by-step explanation:

f(x)=2x^2-44x+185\\\\=2(x^2-2*11*x)+185\\\\=2(x^2-2*11*x+11^2)+185-2*121\\\\\boxed{f(x)=2(x-11)^2-57}\\\\vertex\ is\ (11,-57)

7 0
3 years ago
Read 2 more answers
What is the perimeter of a square with 4 inch sides
notsponge [240]

Answer:

16 units

Step-by-step explanation:

We know a square is 4 sides, and perimeter is the sum of all sides.

4 + 4 + 4 + 4 = 16 units

we can do this in a more efficient way with:

4 x 4 =16 units

8 0
3 years ago
Read 2 more answers
Which of the following vectors are orthogonal to (-1,3)? Check all that apply.
Aliun [14]
First vector orthogonal<span> to ⟨−</span>3<span>,4</span>
7 0
4 years ago
Select from the drop-down menu to explain how to find the quotient of 156.38 and 100.
Blizzard [7]

Answer:

2 places to the left

Step-by-step explanation:

156.38/100 = 1.5638

6 0
3 years ago
The fabric costs$14.00 per yard. If you buy 5 yards or more, you can get 20% off. How much would give yards costs on sale?
ryzh [129]
The answer is $2.80 please give meh a thank you
4 0
4 years ago
Other questions:
  • Slope 3/4 passes through (-4,-3)
    6·1 answer
  • Helen Ming receives a travel allowance of $230 each week from her company for time away from home. If this allowance is taxable
    10·1 answer
  • which measure of central tendency would be best to describe the distribution of hair colors at the mall
    5·1 answer
  • #25 need help ASAP!!!!!
    6·1 answer
  • Rosie wants to make a cube with rectangular blocks each measuring 6cm by 3cm by 8cm. Find the least number of blocks she must us
    12·1 answer
  • Y is directly proportinal to x when y=30 x=6 work out an equation connecting y and x
    13·2 answers
  • A crew of highway workers paved 3/21 mile in 15 minutes. If they continue working at the same rate, what portion of a mile will
    6·1 answer
  • The marked price of a cellphone is $140 after a markup of 25%. Calculate i.) the cost price for this phone. [2]
    12·1 answer
  • Graph -5x+2y=-10<br> NEED HELP PLEASE
    14·1 answer
  • Which is a graph of a proportional relationship? NO BITLY ITS A SCAM I KNOW IT
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!