SOLUTION: For each of the following functions, write the formula for the function's inverse. a.) f(x)=4(2.6)^x where y=f(x) b.) f(x)=log(x/21) where y=f(x)

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: For each of the following functions, write the formula for the function's inverse. a.) f(x)=4(2.6)^x where y=f(x) b.) f(x)=log(x/21) where y=f(x)       Log On


   

Question 1136442: For each of the following functions, write the formula for the function's inverse.
a.) f(x)=4(2.6)^x where y=f(x)

b.) f(x)=log(x/21) where y=f(x)
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

For each of the following functions, write the formula for the function's inverse.
a.)
f%28x%29=4%282.6%29%5Ex+where y=f%28x%29
y=4%282.6%29%5Ex+....swap x and y
x=4%282.6%29%5Ey+....solve or y
x%2F4=%282.6%29%5Ey+.....take log of both sides
log%28x%2F4%29=log%28%282.6%29%5Ey%29+
log%28x%2F4%29=ylog%282.6%29+
y=log%28%28x%2F4%29%29%2Flog%28%282.6%29%29
f%5E-1%28x%29=log%28%28x%2F4%29%29%2Flog%28%282.6%29%29




b.)
f%28x%29=log%2810%2C%28x%2F21%29%29 where y=f%28x%29
y=log%2810%2C%28x%2F21%29%29
x=log%2810%2C%28y%2F21%29%29....recall that log%28b%2C%28y%29+%29=+x is equivalent to (means the exact same thing as) y+=+b%5Ex
y+%2F21=+10%5Ex
y=21%2A10%5Ex
f%5E-1%28x%29=21%2A10%5Ex