Find a formula for the inverse of the function.
y = ln(x + 1)
inverse of y = ln(x+1) is
x = ln(y+1)
changing this back into function form
e^x = y+1
y = e^x - 1
testing:
let x = 5
then y = ln 6 = appr 1.79
into the inverse
y = e^1.79 - 1 = 4.989 , (should be 5 , but not bad! )
Well, you know what they say about formulas and inverse functions, right? They go together like peanut butter and jelly, or in this case, like Bert and Ernie. So let's figure out the inverse of this logarithmic function.
To start, let's switch the roles of x and y. So we now have x = ln(y + 1). Now, to get rid of that pesky natural logarithm, we'll exponentiate both sides. That gives us e^x = y + 1.
Finally, solving for y, we can express the inverse function as y = e^x - 1. Ta-da! The inverse function of y = ln(x + 1) is y = e^x - 1. Now all that's left is to celebrate with a big plate of cookies.
To find the inverse of the function y = ln(x + 1), we'll begin by swapping x and y and solving for y.
Step 1: Swap x and y in the equation:
x = ln(y + 1)
Step 2: Rewrite the equation in exponential form:
e^x = y + 1
Step 3: Subtract 1 from both sides of the equation:
e^x - 1 = y
Therefore, the inverse of the function y = ln(x + 1) is:
y = e^x - 1
To find the inverse of the function y = ln(x + 1), we need to switch the roles of x and y and then solve for y. The steps are as follows:
Step 1: Swap x and y:
x = ln(y + 1)
Step 2: Rewrite the equation in exponential form:
e^x = y + 1
Step 3: Solve for y:
y = e^x - 1
Therefore, the inverse function of y = ln(x + 1) is given by:
f^(-1)(x) = e^x - 1