# How do you find the inverse of #f(x) =10^x# and is it a function?

Inverse of

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To find the inverse of ( f(x) = 10^x ), you need to swap the roles of ( x ) and ( y ) and solve for ( y ).

( f(x) = 10^x ) ( y = 10^x )

Swap ( x ) and ( y ): ( x = 10^y )

Now, solve for ( y ) by taking the logarithm of both sides: ( \log_{10}(x) = \log_{10}(10^y) ) ( \log_{10}(x) = y )

So, the inverse function is ( f^{-1}(x) = \log_{10}(x) ). Yes, it is a function, as each input (( x )) corresponds to exactly one output (( y )).

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