How do you find the inverse of f(x)= -log_5 (x-3)?

1 Answer
Jan 2, 2016

Remember Inverse of (x,y) is given by (y,x) we are going to use the same to find the inverse. Step by step procedure is given below.

Explanation:

Inverse of (x,y) is (y,x)

Our process starts by swapping x and y

f(x) = -log_5(x-3)

Remember y and f(x) are the same.

y=-log_5(x-3)

Step 1: Swap x and y

x=-log_5(y-3)

Multiply both sides by -1

-x=log_5(y-3)

Step 2: Solve for y

This requires you to have some knowledge on converting log to exponent form.

log_b(a) = k => a=b^k

log_5(y-3)=-x

y-3=5^-x

Solving for y.

Adding 3 on both sides would do the trick here.

y=5^-x+3

This y is the inverse function and to be represented as f^-1(x)

Our answer f^-1(x) = 5^-x+3