Answer:
1) The inverse of the function f(x)=2^x+6 is: f^(-1) (x)=log(x-6) / log(2)
2) The inverse of the functio f(x)=2^(x+6) is: f^(-1) (x) =log(x) / log(2) - 6
Solution:
1) f(x)=2^x+6
y=f(x)
y=2^x+6
Solving for x: Subtracting 6 both sides of the equation:
y-6=2^x+6-6
y-6=2^x
Applying log both sides of the equation:
log(y-6)=log(2^x)
Applying poperty of logarithm: log(a^b)=b log(a); with a=2 and b=x
log(y-6)=x log(2)
Dividing both sides of the equation by log(2)
log(y-6) / log(2)=x log(2) / log(2)
log(y-6) / log(2)=x
x=log(y-6) / log(2)
Changing "x" by "f^(-1) (x)" and "y" by "x":
f^(-1) (x)=log(x-6) / log (2)
2) f(x)=2^(x+6)
y=f(x)
y=2^(x+6)
Solving for x: Applying log both sides of the equation:
log(y)=log(2^(x+6))
Applying poperty of logarithm: log(a^b)=b log(a); with a=2 and b=x+6
log(y)=(x+6) log(2)
Dividing both sides of the equation by log(2)
log(y) / log(2)=(x+6) log(2) / log(2)
log(y) / log(2)=x+6
Subtracting 6 both sides of the equation:
log(y) / log(2) - 6 = x+6-6
log(y) / log(2) - 6 = x
x=log(y) / log(2) -6
Changing "x" by "f^(-1) (x)" and "y" by "x":
f^(-1) (x)=log(x) / log (2) - 6
Answer:
true
Step-by-step explanation:
??
Answer:
it depends how many hours both of them make but here is what you can do:
Valeria needs to do 2 hours more than Daniel. This is because Daniel makes $18 and hour and Valeria makes only 10. If you do 10*2 or 10+10 you get 20 which is greater than 18. I hope this helps and good luck!
Answer:
The minimum unit cost is 5377
Step-by-step explanation:
Note that we have a cudratic function of negative principal coefficient.
The minimum value reached by this function is found in its vertex.
For a quadratic function of the form
the x coordinate of the vertex is given by the following expression
In this case the function is:
So:
Then the x coordinate of the vertex is:
So the minimum unit cost is:
Answer:
a = 8 and b = 15
Step-by-step explanation:
I just finished it :D
