Question

how to find the inverse function of

f(x) = tan^-1 (10^x)

Answer 1

wait...the 10^x makes it a little different

y = tan^-1(10^x)
solve for x
tan(y) = 10^x
log(tan(y)) = x

Answer 2

y = tan^(-1)(10^x)
tan(y) = 10^x
log((tany) = x

Answer 3

notice we used log base 10, you could have used natural log but it would have been one more step..

Answer 4

y = tan^(-1)(10^x)
tan(y) = 10^x
ln(tan(y)) = ln(10^x)
ln(tan(y)) = x*ln(10)
(ln(tan(y))/(ln(10)) = x

Answer 5

so since we got to here log((tany) = x
we "should" switch the x and y and then say y = f(x) so.
f(x) = log(tan(x))

Answer 6

thx for the detailed explanation :)