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
How do I find out what is the end behavior diagram for πx^7-x^5-5x+6
stich3 [128]
It is really simple, although maybe not completely intuitive...however the end behavior of any function can be seen as the value that the function would approach as if only the highest powered variable existed...

In this case the end behavior will be that of πx^7 as x→±oo

Since this is an odd power, and has a positive coefficient, π, the end behavior will be:

f(x)→-oo as x→-oo  and f(x)→+oo as x→+oo
3 0
3 years ago
A parabola passes through (7,42) and has a vertex at (-2,6).
Serggg [28]

Answer: To solve this you need to use the vertex form of the equation of a parabola which is y=a(x−h)2+k , where (h,k) are the coordinates of the vertex.

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Simplify<br> 0.75 (0.25f-1.5)
attashe74 [19]

Answer:

3 * (f - 6) / 16

Step-by-step explanation:

8 0
3 years ago
How do you solve x/-11 &gt;= -9?
viktelen [127]
Multiply -11 on both sides, which would leave you with x=99
x=99
8 0
4 years ago
8-7x- x2 x+5/х+8 9x -9<br><br><br> Every step on how you got your answer.
Mrac [35]

Answer:11

Step-by-step explanation:

8 0
3 years ago
Other questions:
  • I need help with this integral question! It is short and easy if you know what you're doing. Due in an hour! Thanks!!!
    5·1 answer
  • A direct variation function contains the points (2, 14) and (4, 28). Which equation represents the function?
    15·2 answers
  • In the standard equation of a circle, what represents the center of the circle and the radius?
    11·1 answer
  • The formula for the volume of a pyramid is V=1/3Bh. Which of the following equations is equivalent to the given formula?
    12·2 answers
  • URGENT :find x and y please thank youuuu
    13·1 answer
  • What is the slope of this line?
    10·1 answer
  • 9. Marco has a dog that weighs 5 times as much as John's cat. The total weight of both animals is 72
    9·1 answer
  • Which equation is equivalent to 1/5x - 3 = 2/3
    9·1 answer
  • A picture is 5 inches wide and 8 inches tall:
    7·1 answer
  • For this item, any non-integer answer should be entered as a decimal, rounded to the hundredths place.
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!