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Lunna [17]
3 years ago
13

Inverse Function In Exercise,analytically show that the functions are inverse functions.Then use the graphing utility to show th

is graphically.
f(x) = e^x - 1
g(x) = In(x + 1)

Mathematics
1 answer:
Anna [14]3 years ago
4 0

Step-by-step explanation:

We need to show whether

f^{-1}(x) = g(x)

or

g^{-1}(x) = f(x)

so we'll do either one of them,

we'll convert f(x) to f^-1(x) and lets see if it looks like g(x).

f(x) = e^x - 1

we can also write it as:

y = e^x - 1

now all we have to do is to make x the subject of the equation.

y+1 = e^x

\ln{(y+1)} = x

x=\ln{(y+1)}

now we'll interchange the variables

y=\ln{(x+1)}

this is the inverse of f(x)

f^{-1}(x)=\ln{(x+1)}

and it does equal to g(x)

g(x)=\ln{(x+1)}

Hence, both functions are inverse of each other!

This can be shown graphically too:

we can see that both functions are reflections of each other about the line y=x.

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Answer:

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Step-by-step explanation:

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3 years ago
Use an equation to find the value of k so that the line that passes through the given slope (1,3) , (5,k) m=2
scoray [572]

Answer:

The value of k with given points and slop = 11

Step-by-step explanation:

Given that a line passes through two points having slop (m) = 2

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Now slop of line can be written as,

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Or, m =  \frac{(y2 - y1)}{(x2 - x1)}

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Or, 2 =  \frac{(k - 3)}{(4)}

So , k - 3 = 8

∴ K = 8+3 = 11

Hence the value of k with given points and slop = 11    Answer

5 0
3 years ago
As an estimation we are told 5 miles is 8 km.<br> Convert 40 miles to km.
sergeinik [125]

Answer:

5 miles=8 km

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So, 40 miles is 64 km.

Step-by-step explanation:

7 0
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