# How do you find the inverse of #f(x)=4^x# and is it a function?

By signing up, you agree to our Terms of Service and Privacy Policy

To find the inverse of ( f(x) = 4^x ), we first interchange the roles of ( x ) and ( y ), then solve for ( y ).

So, let ( y = 4^x ).

Interchange ( x ) and ( y ): ( x = 4^y ).

Now, solve for ( y ): [ \log_4{x} = y ]

Hence, the inverse function is ( f^{-1}(x) = \log_4{x} ).

Yes, ( f(x) = 4^x ) is a function because for each input ( x ), there is exactly one output ( f(x) ).

By signing up, you agree to our Terms of Service and Privacy Policy

To find the inverse of the function ( f(x) = 4^x ), we switch the roles of ( x ) and ( y ) and solve for ( y ).

- Replace ( f(x) ) with ( y ): ( y = 4^x ).
- Swap ( x ) and ( y ): ( x = 4^y ).
- Solve for ( y ): [ \log_4(x) = y ]

Thus, the inverse function of ( f(x) = 4^x ) is ( f^{-1}(x) = \log_4(x) ).

As for whether the inverse function is a function, yes, ( f^{-1}(x) = \log_4(x) ) is a function. Each input ( x ) corresponds to exactly one output ( y ), which fulfills the definition of a function.

By signing up, you agree to our Terms of Service and Privacy Policy

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.

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.

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.

- How do you find the Vertical, Horizontal, and Oblique Asymptote given #f(x)= 1/(x-2)#?
- How do you find the horizontal asymptote for #y = (x + 1)/(x - 1)#?
- How do you determine if #F(x)=x^3-x # is an even or odd function?
- How do you find the vertical, horizontal and slant asymptotes of: #f(x)=sinx/(x(x^2-81))#?
- How do I find the vertical asymptotes of #f(x) = tanπx#?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7