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3 years ago

Whenever a,x,y are positive integers, which of the following expressions is equivalent to x^ay^a

Mathematics

1 answer:

lilavasa [31]3 years ago

3 0

Answer:

${(xy)}^{a}$

Step-by-step explanation:

when the exponent is equal, we can put the x and y together in a bracket and a as the Exponent of xy.

Hope I get your question~

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PLEASE HELP!!!! Which of these pair of functions are inverse functions?

Mamont248 [21]

Answer:

Option B and C are correct.

Step-by-step explanation:

Inverse function: If both the domain and the range are R for a function f(x), and if f(x) has an inverse g(x) then:

$f(g(x)) = g(f(x)) = x$ for every x∈R.

Let $f(x) = \frac{1}{2}(\ln(\frac{x}{2}) -1)$ and $g(x) = 2e^{2x+1}$

Use logarithmic rules:

$ln e^a = a$

$e^{lnx} = x$

$\ln a^b = b\ln a$

then, by definition;

$f(g(x)) = f(2e^{2x+1}) =\frac{1}{2}(\ln(\frac{2e^{2x+1}}{2})-1)$ = $\frac{1}{2}(\ln(e^{2x+1}}){-1) = \frac{1}{2} (2x+1-1) =\frac{1}{2}(2x) = x$

$g(f(x)) = g(\frac{1}{2}(\ln(\frac{x}{2}) -1)) = 2e^{2({\frac{1}{2}(\ln(\frac{x}{2}) -1})+1$ $2e^{(\ln(\frac{x}{2}) -1+1}=2e^{\ln(\frac{x}{2})} =2\cdot \frac{x}{2} = x$

Similarly;

for $f(x) = \frac{4 \ln(x^2)}{e^2}$ and $g(x) = e^{\frac{e^2 \cdot x}{8} }$

then, by definition;

$f(g(x)) = f(e^{\frac{e^2 \cdot x}{8}}) =\frac{4 \ln {(\frac{e^2 \cdot x}{8})^2}}{e^2}$ = $\frac{8 \ln {(\frac{e^2 \cdot x}{8})}}{e^2} =\frac{8\frac{e^2\cdot x}{8} }{e^2}=\frac{8e^2 \cdot x}{8e^2}=x$

Similarly,

g(f(x)) = x

Therefore, the only option B and C are correct. As the pairs of functions are inverse function.

3 0

4 years ago

ASAP HELP This is due today so answer correct and I have attempt to do your best

Kamila [148]

Answer:

3) x-axis: 1 unit

y-axis: 10 units

4) quadrant II

coordinates: (-2, 4)

7) Quadrants I and IV; time is always positive , but temperature can be positive and negative

8) W = (-0.75, -1)

Step-by-step explanation:

3) x-axis: 1 unit

y-axis: 10 units

4) quadrant II

coordinates: (-2, 4)

7) Quadrants I and IV; time is always positive , but temperature can be positive and negative

8) W = (-0.75, -1)

5 0

2 years ago

Complete the pattern, 1.1, 2.2, 3-3. What is the rule?

spin [16.1K]

You mean 3.3? If that is the case then:

an=1.1+1(n-2)

or an=an-1+1
a1= 1.1

5 0

3 years ago

A 5 lb. bag of organic all-purpose flour costs $6.76. What is the unit price? _ per pound

Sonbull [250]

for 5 lb. bag = $6.76

so, for 1 lb. bag = 6.76/5 = $1.35

So, unit prize is $1.35 per pound.

7 0

3 years ago

Read 2 more answers

Find the measure of DC if m

kupik [55]

Answer:

B. 132°

Step-by-step explanation:

Find the measure of arc BD

m∠A = 1/2(arc BC - arc BD)
2*36° = 150° - arc BD
arc BD = 150° - 72° = 78°

Find the measure of arc DC

arc BD + arc BC + arc DC = 360°

arc DC = 360° - (150° + 78°) = 360° - 228° = 132°

Correct choice is B

7 0

3 years ago