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3 years ago

For the functions f(x) = 5x − 3 and g(x) = x + 4, which composition produces the greatest output?

1 answer:

7 0

You could actually find the compositions and thus have something to compare. You haven't shared the list of possible answer choices.

(f+g)(x) = 5x - 3 + x + 4 = 6x + 1

(f-g)(x) = 5x - 3 - x - 4 = 4x - 7

(f*g)(x) = (5x-3)((x+4) = 5x^2 + 20x - 3x - 12 = 5x^2 + 17x - 12

There are also the quotient (f/g)(x) and the compositions f(g(x)) and g(f(x)).

WRite them out.

Then you could arbitrarily select x values, such as 2, 10, etc., subst. them into each composition and determine which output is greatest.

You might be interested in

The sum of first three terms of a finite geometric series is -7/10 and their product is -1/125. [Hint: Use a/r, a, and ar to rep

Alchen [17]

Ooh, fun

geometric sequences can be represented as
$a_n=a(r)^{n-1}$
so the first 3 terms are
$a_1=a$
$a_2=a(r)$
$a_2=a(r)^2$

the sum is -7/10
$\frac{-7}{10}=a+ar+ar^2$
and their product is -1/125
$\frac{-1}{125}=(a)(ar)(ar^2)=a^3r^3=(ar)^3$

from the 2nd equation we can take the cube root of both sides to get
$\frac{-1}{5}=ar$
note that a=ar/r and ar²=(ar)r
so now rewrite 1st equation as
$\frac{-7}{10}=\frac{ar}{r}+ar+(ar)r$
subsituting -1/5 for ar
$\frac{-7}{10}=\frac{\frac{-1}{5}}{r}+\frac{-1}{5}+(\frac{-1}{5})r$
which simplifies to
$\frac{-7}{10}=\frac{-1}{5r}+\frac{-1}{5}+\frac{-r}{5}$
multiply both sides by 10r
-7r=-2-2r-2r²
add (2r²+2r+2) to both sides
2r²-5r+2=0
solve using quadratic formula
for $ax^2+bx+c=0$
$x=\frac{-b \pm \sqrt{b^2-4ac}}{2a}$
so
for 2r²-5r+2=0
a=2
b=-5
c=2

$r=\frac{-(-5) \pm \sqrt{(-5)^2-4(2)(2)}}{2(2)}$
$r=\frac{5 \pm \sqrt{25-16}}{4}$
$r=\frac{5 \pm \sqrt{9}}{4}$
$r=\frac{5 \pm 3}{4}$
so
$r=\frac{5+3}{4}=\frac{8}{4}=2$ or $r=\frac{5-3}{4}=\frac{2}{4}=\frac{1}{2}$

use them to solve for the value of a
$\frac{-1}{5}=ar$
$\frac{-1}{5r}=a$
try for r=2 and 1/2
$a=\frac{-1}{10}$ or $a=\frac{-2}{5}$

test each
for a=-1/10 and r=2
a+ar+ar²= $\frac{-1}{10}+\frac{-2}{10}+\frac{-4}{10}=\frac{-7}{10}$
it works

for a=-2/5 and r=1/2
a+ar+ar²= $\frac{-2}{5}+\frac{-1}{5}+\frac{-1}{10}=\frac{-7}{10}$
it works

both have the same terms but one is simplified

the 3 numbers are $\frac{-2}{5}$ , $\frac{-1}{5}$ , and $\frac{-1}{10}$

6 0

3 years ago

Solve. 24= 7/8g A. 3/7 B. 21 C. 23 1/8 D. 27 3/7

Mrac [35]

I hope this helps you

3 0

2 years ago

Read 2 more answers

Which is the inverse of this matrix? A. B. C. D. E. The matrix is noninvertible.

kvasek [131]

Answer:

-19 9 7

[15 -7 6 ]

-2 1 1

Step-by-step explanation:

8 0

2 years ago

Read 2 more answers

Write the following equation in standard form:22+52 +4 24 - 220

LekaFEV [45]

Answer:2.78×10^2

Step-by-step explanation:

22+52+424-220

=278

In standard form

=2.78×10^2

6 0

2 years ago

Determine if the triangle with the given sides is acute, obtuse, or right. 36, 49, 60

kotykmax [81]

When given 3 triangle sides, to determine if the triangle is acute, right or obtuse:
1) Square all 3 sides.
2) Sum the squares of the 2 shortest sides.
3) Compare this sum to the square of the 3rd side.

if sum > 3rd side² Acute Triangle
if sum = 3rd side² Right Triangle
if sum < 3rd side² Obtuse Triangle

1) 1,296 2,401 3,600
2) Sum = 3,697
3) 3,697 is greater than 3,600
Therefore, the triangle is acute.

Source:
http://www.1728.org/triantest.htm

4 0

2 years ago