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How do you find the inverse of #f(x) =10^x#?

Answer 1

Caleb Alexander

To find the inverse of the function ( f(x) = 10^x ), follow these steps:

Replace ( f(x) ) with ( y ).
Swap the variables ( x ) and ( y ).
Solve the equation for ( y ).
Replace ( y ) with ( f^{-1}(x) ).

Starting with ( y = 10^x ):

Swap variables: ( x = 10^y ).
Solve for ( y ): ( \log_{10}(x) = y ).
Replace ( y ) with ( f^{-1}(x) ): ( f^{-1}(x) = \log_{10}(x) ).

So, the inverse of ( f(x) = 10^x ) is ( f^{-1}(x) = \log_{10}(x) ).

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Answer 2

James Allen

#f^(-1)(x)=logx#

By definition, #y=f^(-1)(x)ifff(y)=x#

#iff10^y=x#

#iffy=logx#

Hence the original function looks like this graph{10^x [-12.22, 5.555, -1.634, 7.25]}

The inverse function looks like this graph{logx [-2.71, 13.09, -5.796, 2.1]}

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.