Inverse Functions
This is the inverse of y=3x-4
What is
f^-1(x)=1/3x+4/3
This is the solution to
(1/2)^k=4
This is the one word definition of a logarithm.
What is "an exponent".
A skydiver in free fall travels at a speed modeled by the equation below. This is the time taken to attain a speed of 147 ft/sec (100 mph).
v(t)=176(1-e^(-0.18t))
What is 10 seconds
This is what a function must be to have an inverse.
What is one-to-one
This is the inverse of f(x)=x^3+1
What is
f^-1(x)=root(3)(x-1)
This is the solution to
2^(3-y)=8
What is
{0}
This is the equivalent logarithmic form of
(2/3)^-3=27/8
What is
log_(2/3)(27/8)=-3
This is the time needed for $5000 to increase to $18,000 at 6.8% annual interest compounded continuously.
What is 18.8 years
This can be written in exponential form as
ln(sqrte)=1/2
What is
e^(1/2)=sqrt(e)
This is the inverse of f(x)=1/(x-3)
What is
f^-1(x)=(1+3x)/x
This is the solution to
e^(4x-1)=(e^2)^x
What is
{1/2}
This is the base of the logarithmic function whose graph contains the point (81,4).
What is 3
For any amount of money invested at 6.8% annual interest compounded continuously, this is how long will it take to triple.
What is 16.2 years
This is the solution to log_2x+log_2(x+2)=3
What is {2}
If two functions are inverses of each other, then their graphs are symmetric around this.
What is the line
y=x
This has an exact solution:
3^(2x-5)=13
What is
x=1/2(5+(ln13)/(ln3))
This logarithm can be rewritten in simplified form.
log_7(7k+5r^2)
What is cannot be simplified
This is the amount of time for any amount of money invested at 6.8% annual interest compounded continuously to triple.
What is 16.2 years
This is the half-life of the radioactive material modeled by A(t)=600e^(-0.05t)
What is 13.9 days
This is the inverse of the function
f(x)=sqrt(25-x^2)
What is f has no inverse.
This is an exact solution to
e^(4x)=4^(x-2)
What is (-2ln(2))/(2-ln(2))
This is the solution to
ln[ln(e^-x)]=ln3
What is -3
This is the half-life of radioactive material modeled by
A(t)=600e^(-0.05t)
What is 329.3 grams