Find the inverse function of f(x) =e^x+1
To find the inverse function of f(x) = e^x + 1, we can use algebraic method as follows:
Step 1: Replace f(x) with y: y = e^x + 1
Step 2: Swap x and y: x = e^y + 1
Step 3: Solve for y: x - 1 = e^y
Step 4: Take the natural logarithm of both sides: ln(x - 1) = y
Step 5: Swap y and x to obtain the inverse function: f^(-1)(x) = ln(x - 1)
Therefore, the inverse function of f(x) = e^x + 1 is f^(-1)(x) = ln(x - 1).
To find the inverse function of f(x) = e^x+1, we need to switch the x and y variables and solve for y.
Step 1: Replace f(x) with y
y = e^x+1
Step 2: Swap x and y
x = e^y+1
Step 3: Solve for y
Subtract 1 from both sides:
x - 1 = e^y
Step 4: Take the natural logarithm (ln) of both sides to remove the exponential function
ln(x - 1) = ln(e^y)
Step 5: Use the property that ln(e^y) = y to simplify the equation
ln(x - 1) = y
Step 6: Switch y back to f^-1(x) to get the inverse function
f^-1(x) = ln(x - 1)
Therefore, the inverse function of f(x) = e^x+1 is f^-1(x) = ln(x - 1).