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3 years ago

What is the range of the function f(x) = 3.2x for the domain {-4, -2, 0, 2, 4}?

1 answer:

5 0

The range are all the possible solutions for y. Since the domain is given, these are all the possible x values. To find the range, we can simply substitute each of these x values to the given function f(x) = 3.2x.

Given the domain, we use this to find the range values,
Domain: {-4, -2, 0, 2, 4}
Range: {-12.8, -6.4, 0, 6.4, 12.8}

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Suppose h(x)=3x-2 and j(x) = ax +b. Find a relationship between a and b such that h(j(x)) = j(h(x))

sergejj [24]

Answer:

$\displaystyle a = \frac{1}{3} \text{ and } b = \frac{2}{3}$

Step-by-step explanation:

We can use the definition of inverse functions. Recall that if two functions, f and g are inverses, then:

$\displaystyle f(g(x)) = g(f(x)) = x$

So, we can let j be the inverse function of h.

Function h is given by:

$\displaystyle h(x) = y = 3x-2$

Find its inverse. Flip variables:

$x = 3y - 2$

Solve for y. Add:

$\displaystyle x + 2 = 3y$

Hence:

$\displaystyle h^{-1}(x) = j(x) = \frac{x+2}{3} = \frac{1}{3} x + \frac{2}{3}$

Therefore, a = 1/3 and b = 2/3.

We can verify our solution:

$\displaystyle \begin{aligned} h(j(x)) &= h\left( \frac{1}{3} x + \frac{2}{3}\right) \\ \\ &= 3\left(\frac{1}{3}x + \frac{2}{3}\right) -2 \\ \\ &= (x + 2) -2 \\ \\ &= x \end{aligned}$

And:

$\displaystyle \begin{aligned} j(h(x)) &= j\left(3x-2\right) \\ \\ &= \frac{1}{3}\left( 3x-2\right)+\frac{2}{3} \\ \\ &=\left( x- \frac{2}{3}\right) + \frac{2}{3} \\ \\ &= x \stackrel{\checkmark}{=} x\end{aligned}$

3 0

2 years ago

I would love help and thank you

tigry1 [53]

The formula is width times length

5 0

3 years ago

Read 2 more answers

Please help me with this question.

elixir [45]

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8 0

3 years ago

arsen [322]

Answer:

Step-by-step explanation:

3*-4

3 0

3 years ago

Edgar has taken out a $6,250 unsubsidized Stafford loan to fund his four-year undergraduate degree. The loan has a duration of 1

abruzzese [7]

The present worth of the loan is $6,250
The start of payment will after 4 years
The nominal interest rate is 6.1% compounded monthly which is equal to 6.27% effective.

The future worth (after graduation) of the loan is
F = $6,250 (1 + 0.0627)^4 = $7,971.18

The interest is
$7,971.18 - $6,250 = $1,721.18
I didn't round off when solving these so it's not the exact answer among the choices but the closest is letter B $1,722.22

5 0

3 years ago