Lucy bought some shrubs to plant in a garden.Eaxh shrub cost $9.If lucy spent $216bin all, how many shrubs did she buy

4. Determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

Ierofanga [76]

Answer:

YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

Step-by-step explanation:

Given

Given that the function f(x) and g(x) are inverse functions.

$f\left(x\right)\:=\:\frac{1}{3}x\:+\:5$

$g(x) = 3x - 15$

To determine

Let us determine whether f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

<u>Determining the inverse function of f(x) </u>

A function g is the inverse function of f if for y = f(x), x = g(y)

$y=\frac{1}{3}x+5$

Replace x with y

$x=\frac{1}{3}y+5$

Solve for y

$y=3x-15$

Therefore,

YES! we conclude that f(x) = 1/3x + 5 and g(x) = 3x - 15 are inverse functions.

4 0

2 years ago

Let V=ℝ2 and let H be the subset of V of all points on the line 4x+3y=12. Is H a subspace of the vector space V?

sergejj [24]

Answer:

No, it isn't.

Step-by-step explanation:

We have $V=IR^{2}$ and let $H$ be the subset of $V$ of all points on the line

$4x+3y=12$

We need to find if $H$ is a subspace of the vector space $V$ .

In $IR^{2}$ all the possibilities for own subspace of the vector space $IR^{2}$ are :

$IR^{2}$ itself.

The vector $0_{IR^{2}}=\left[\begin{array}{c}0&0\end{array}\right]$

All lines in $IR^{2}$ that passes through the origin ( $0_{IR^{2}}=\left[\begin{array}{c}0&0\end{array}\right]$ )

We know that $H$ is the subset of $IR^{2}$ of all points on the line $4x+3y=12$

If we look at the equation, the point $\left[\begin{array}{c}0&0\end{array}\right]$ doesn't verify it because :

$4x+3y=12\\4(0)+3(0)=12\\0=12$

Which is an absurd. Therefore, $H$ doesn't contain the origin (and $H$ is a line in $IR^{2}$ ). Finally, it can't be a vector space of $V=IR^{2}$

8 0

3 years ago

Uncle Howard left his only niece 56% of his assets according to his will. If his totaled assets

damaskus [11]

Answer:

$315,840.00

Step-by-step explanation:

$564,000 x 0.56 = $315,840.00

4 0

3 years ago

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Michael is paid $9 per hour to work at the movie theater and $7 per hour when he helps his aunt at her bakery. Michael cannot wo

evablogger [386]

if he works at the theater he can make $288 in 32 hours, if he works at his aunts he can make $224 in 32 hours. he should work at the theater to meet his goal.

I really hope this helps

4 0

3 years ago

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Let y=3t+6 be a linear function representing the distance, in feet, from home for an ant t minutes after starting out from a loc

Marysya12 [62]

Answer:

The y, in the equation, represents the total distance, in feet, from an ant t minutes after starting out from a location near its home. The 6 represents the the distance of the location where the ant starts traveling. The 3 represents the amount of feet covered in one minute. That's why when you increase the minute by one (experiment!!), the distance away from home increases by three, and that means that the ant is traveling at 3 ft/minute. (lol crazy)

3 = the ant's speed in ft/minute

6 0

3 years ago

Read 2 more answers