Find the inverse function of
F(x)= 3e^(2x)
I found y=lnx/6 Am I right ? Thanks
nope.
x = 3e^(2y)
x/3 = e^(2y)
ln(x/3) = 2y
y = 1/2 ln(x/3) = ln(x/3)^(1/2) = ln√(x/3)
Better review properties of logs and powers.
Thanks, I get it now
To find the inverse function of F(x) = 3e^(2x), we need to switch the roles of x and y and solve for y.
Step 1: Swap x and y in the equation:
x = 3e^(2y)
Step 2: Solve for y:
Divide both sides by 3:
x/3 = e^(2y)
Step 3: Take the natural logarithm of both sides:
ln(x/3) = 2y
Step 4: Divide both sides by 2:
ln(x/3)/2 = y
So, the inverse function of F(x) = 3e^(2x) is given by:
f^(-1)(x) = ln(x/3)/2
Therefore, your answer is not correct. The correct inverse function is f^(-1)(x) = ln(x/3)/2.