I am lost!! Find the inverse function of f(x)=log2(4x) Thanks
Remember the steps of finding the inverse.
y = log2 (4x)
step 1. interchange the x and y variables:
x = log2 (4y)
step2. solve this new equation for y
x = log2 (4y) -----> 2^x = 4y , by definition
y = (1/4)(2^x)
= 2^-2 (2^x)
= 2^(x-2)
f^-1 (x) = 2^(x-2)
or
change the original to exponential form:
y = log2 (4x) ----> 2^y = 4x
inverse ----> 2^x = 4y
y = (1/4)(2^x) = 2^(x-2)
Hey there, Lost Explorer! Don't worry, I've got your back! To find the inverse function of f(x) = log2(4x), we'll need to switch the x and y variables and solve for y. So let's get juggling!
Step 1: Replace f(x) with y:
y = log2(4x)
Step 2: Swap the x and y variables:
x = log2(4y)
Step 3: Eliminate the logarithm by rewriting it in exponential form:
2^x = 4y
Step 4: Solve for y by dividing both sides by 4:
y = (1/4) * 2^x
And there you have it, Lost Explorer! The inverse function of f(x) = log2(4x) is g(x) = (1/4) * 2^x. Now you can find your way back with some mathematical chuckles!
To find the inverse function of f(x) = log2(4x), follow these steps:
Step 1: Replace f(x) with y:
y = log2(4x)
Step 2: Switch x and y:
x = log2(4y)
Step 3: Rewrite the equation in exponential form:
2^x = 4y
Step 4: Divide both sides of the equation by 4:
2^x/4 = y
Step 5: Replace y with f^(-1)(x) (the inverse function):
f^(-1)(x) = 2^x/4
Therefore, the inverse function of f(x) = log2(4x) is f^(-1)(x) = 2^x/4.
To find the inverse function of f(x) = log2(4x), we need to swap the x and y variables and then solve for y.
Step 1: Swap x and y
x = log2(4y)
Step 2: Solve for y
To isolate y, we need to get rid of the logarithm. In this case, we can raise 2 to the power of both sides of the equation:
2^x = 4y
Step 3: Simplify
To simplify further, divide both sides of the equation by 4:
2^x/4 = 2^2y
2^x/4 = 2^(2y)
Step 4: Equate exponents
Now, we can equate the exponents on both sides of the equation:
x/4 = 2y
Step 5: Solve for y
To isolate y, divide both sides of the equation by 2:
y = x/8
Therefore, the inverse function of f(x) = log2(4x) is given by f^(-1)(x) = x/8.