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:
3.78
Step-by-step explanation:
Answer:
C. (4,28)
Step-by-step explanation:
The substitution method requires you to input a specified number in place of a variable. In this case, the variable 'x' should be replaced by the number 4. Using the order of operations, we know that multiplication should be applied before subtraction. When we replace 'x' with 4, we get the equation 'y=8(4)-4'. Multiplying 8 and 4 gives us 32. If we subtract 4 from 32, we get 28. The answer ends up being 'y=28'.
That is the first part of our solution. What we are actually looking for is an ordered pair. We know ordered pairs are written in the form (x, y). First, we need to find the 'x'. The 'x' has been given to us from the beginning, it is 4. Next is the 'y'. This is what we needed to find using substitution. We ultimately concluded that the 'y' is equivalent to 28. Therefore our ordered pair is (4, 28), the letter choice C.
I hope this helped you and that I clearly elaborated on the answer choice.
Step-by-step explanation:
for measuring the angle use the protractor !
6506 or 656 is the answer
