What is the invers of:
y=2log(x+1)
and please explain this to me..not just an answer.
What you want is an equation for x in terms of y. That will be the inverse functuon.
I will assume that the log is to base e.
y = ln (x+1)^2
e^y = (x+1)^2
x+1 = sqrt (e^y) = e^(y/2)
x = e^(y/2) - 1
Switching variables, the inverse function can be written
f^-1(x) = e^(x/2) -1
thanks
inverse of y=ln(x)+4
how would i do this?
To find the inverse of the function y = 2log(x+1), we need to follow a few steps:
Step 1: Replace y with x and x with y:
x = 2log(y+1)
Step 2: Solve the equation for y:
x = 2log(y+1)
Divide both sides by 2:
x/2 = log(y+1)
Step 3: Rewrite the equation in exponential form:
y + 1 = 10^(x/2)
Subtract 1 from both sides:
y = 10^(x/2) - 1
Therefore, the inverse of the function y = 2log(x+1) is given by y = 10^(x/2) - 1.
Now, let's understand the steps involved in finding the inverse:
Step 1: In this step, we replace y with x and x with y to interchange their positions. This allows us to solve for the new variable y.
Step 2: We manipulate the equation to isolate the logarithmic term. By dividing both sides by 2, we move the logarithm to one side of the equation.
Step 3: In this step, we rewrite the equation in exponential form by taking the base 10 logarithm. This allows us to solve for y by isolating it on one side of the equation.
By following these steps, we obtained the inverse function y = 10^(x/2) - 1, which represents the original function reversed.