All categories

4 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

Given: y varies directly with x and has a constant rate of change of 7. When the value of y is 12, then the value of x would be

docker41 [41]

Y = kx is the direct variation equation, where 'k' is the constant of variation.
12 = 7(x)
Divide both sides by 7
12/7 = x

7 0

3 years ago

Read 2 more answers

How do you do this?please help

d1i1m1o1n [39]

Answer:

10.5 ft.

Step-by-step explanation:

1. Find the radius of the larger circle

4/7 = 3/r --> the ratio should be <em>constant</em>

cross-multiplication: <em>21 = 4r</em>

Divide: <em>r = 5.25 ft.</em>

2. Find the circumference

Equation: <em>C = 2πr</em>

C = <em>2π*5.25</em>

C = 10.5π ft.

7 0

4 years ago

40⋅8−10^2 what is the result

Liono4ka [1.6K]

Answer:

220

Step-by-step explanation:

40 x 8 = 320, and 10 squared is 100. 320 - 100 = 220.

7 0

3 years ago

Read 2 more answers

(b). Solve for x and verify the result: 5x + 3 = 4/3 (1+x)

Kazeer [188]

<h2><u>Solution :</u></h2>

${\dashrightarrow\sf{5x + 3 = \dfrac{4}{3} \bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{3 \bigg(5x + 3 \bigg)= 4\bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{\bigg(5x \times 3 + 3 \times 3 \bigg)= \bigg(1 \times 4 + x \times 4 \bigg)}}$

${\dashrightarrow\sf{\bigg(15x + 9 \bigg)= \bigg(4 + 4x\bigg)}}$

${\dashrightarrow\sf{15x - 4x =4 - 9 }}$

${\dashrightarrow\sf{11x =4 - 9 }}$

${\dashrightarrow\sf{11x = - 5 }}$

${\dashrightarrow\sf{x = - \dfrac{5}{11}}}$

$\bigstar{\underline{\boxed{\sf{\red{x = - \dfrac{5}{11}}}}}}$

<u>∴ The value of x is -5/11.</u>

$\begin{gathered}\end{gathered}$

<h3><u>Verification :</u></h3>

${\dashrightarrow\sf{5x + 3 = \dfrac{4}{3} \bigg(1 + x \bigg)}}$

${\dashrightarrow\sf{ \bigg(\left\{5 \times - \dfrac{5}{11} \right\} + 3 \bigg)= \dfrac{4}{3} \bigg(1 + \left\{ - \dfrac{5}{10}\right\}\bigg)}}$

${\dashrightarrow\sf{ \bigg(\left\{- \dfrac{25}{11} \right\} + 3 \bigg)= \dfrac{4}{3} \bigg(1 + \left\{ - \dfrac{5}{11}\right\}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{ - ( 25 )+ (3 \times 11)}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{(1 \times 11) - (5 \times 1)}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{ - 25+ 33}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{11 - 5}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \dfrac{4}{3} \bigg( \dfrac{6}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{4}{3} \times \dfrac{6}{11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{4 \times 6}{3 \times 11}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\dfrac{24}{33}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg(\cancel{\dfrac{24}{33}}\bigg)}}$

${\dashrightarrow\sf{ \bigg( \dfrac{8}{11} \bigg)= \bigg({\dfrac{8}{11}}\bigg)}}$

$\bigstar{\underline{\boxed{\sf{\red{LHS = RHS}}}}}$

<u>∴ Hence Verified !</u>

6 0

3 years ago

Read 2 more answers

Between x = 2 and x = 3, which function has the same average rate of change as y = 2x ?

SVEN [57.7K]

Answer:

y= (5)^x - 2

Step-by-step explanation:

What I did to get this answer was.. it said it was between x=2 and x=3 and saw that take away 2 on the outside of the parenthesis and that equaled 3. Basically it wasn't true thinking but that's what i did. I got it right on USATestPrep.

4 0

3 years ago