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3 years ago

The table represents the function f(x).

Mathematics

1 answer:

Eddi Din [679]3 years ago

5 0

Answer:A

Step-by-step explanation:

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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

3 years ago

Two urns each contain green balls and blue balls. urn i contains 4 green balls and 6 blue balls, and urn ii contains 6 green bal

UNO [17]

4+6+6+2=18(balls)
Another way 1)4+6=10(balls)-green and blue
2)6+2=8(balls)-green and blue
3)10+8=18(balls)-total probability

8 0

3 years ago

Read 2 more answers

Find the length of the short leg of a 30-60-90 triangle if the long leg is 3cm

antoniya [11.8K]

Answer:

Short leg = √3 cm

Step-by-step explanation:

the opposite angle of long leg is 60°

hypotenuse : x

sin 60° = 3/x = √3 / 2

x = (3 x 2) / √3 = 2√3

short leg length (s)

Cos 60° = 1/2 = s / x = s / 2√3

s = √3

7 0

3 years ago

What is (0.54)⋅(3.8)=

ra1l [238]

Answer:

2.052

Step-by-step explanation:

I hope it helped lot sj

8 0

2 years ago

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A rectangle has a perimeter of 12 centimeters and a height of 5 centimeters. What is the length of the base?

Gwar [14]

Answer:

1 cm

Step-by-step explanation:

We know that the formula for perimeter is 2(l+w) or l+l+w+w

We know that the height is 5 cm so that means w= 5 also that there is 5 cm on both sides of the rectangle. So 5+5=10 so that means that the length of the rectangle is 1 cm if you add the length together you 2 when you add the width you get 10. 10+2=12.

5 0

2 years ago