SOLUTION: Find the Inverse of the following function: f(x)=10^(x-3)+4

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Question 54968: Find the Inverse of the following function:
f(x)=10^(x-3)+4
Answer by funmath(2873) About Me  (Show Source):
You can put this solution on YOUR website!
Find the Inverse of the following function:
:
f%28x%29=10%5E%28x-3%29%2B4
y=10%5E%28x-3%29%2B4 Switch the x and y and solve for y.
x=10%5E%28y-3%29%2B4
x-4=10%5E%28y-3%29%2B4-4
x-4=10%5E%28y-3%29 Take the log of both sides:
log%28%28x-4%29%29=log%28%2810%5E%28y-3%29%29%29
log%28%28x-4%29%29=%28y-3%29log%2810%29 Note the common log of 10=1
log%28%28x-4%29%29=%28y-3%29%281%29
log%28%28x-4%29%29=y-3
log%28%28x-4%29%29%2B3=y-3%2B3
log%28%28x-4%29%29%2B3=y Replace y with f^-1(x)
f%5E%28-1%29%28x%29=log%28%28x-4%29%29%2B3
Happy Calculating!!!