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3 years ago

If(x)= 2e^x-1 +3 , what is f^-1 (x)

Mathematics

1 answer:

Rainbow [258]3 years ago

4 0

Answer:

f^-1 (x) = 1+ln( (x-3)/2)

Step-by-step explanation:

hello :

let f(x) = y so : y = 2e^(x-1) +3

calculate x : e^(x-1) = (y-3)/2

for : y-3 > 0 : x-1 = ln( (y-3)/2) so : x= 1+ln( (y-3)/2)

If(x)= 2e^(x-1) +3 , what is f^-1 (x) = 1+ln( (x-3)/2)

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olganol [36]

Answer:

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Step-by-step explanation:

Step 1: Add -x to both sides.

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tiny-mole [99]

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Plug in the values for x

Step-by-step explanation:

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3 years ago

Complete parts a through f below to find nonnegative numbers x and y that satisfy the given requirements. Give the optimum value

MArishka [77]

Answer:

y = 81-x
the domain of P(x) is [0, 81]
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Step-by-step explanation:

Given

x plus y equals 81
x and y are non-negative

Find

P equals x squared y is maximized

Solution

a. Solve x plus y equals 81 for y.

y equals 81 minus x

b. Substitute the result from part a into the equation P equals x squared y for the variable that is to be maximized.

P equals x squared left parenthesis 81 minus x right parenthesis

c. Find the domain of the function P found in part b.

left bracket 0 comma 81 right bracket

d. Find dP/dx. Solve the equation dP/dx = 0.

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The zero product rule tells us the solutions to this equation are x=0 and x=54, the values of x that make the factors be zero. x=0 is an extraneous solution for this problem so ...

P is maximized at (x, y) = (54, 27).

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3 years ago