15Twilight
Answered

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If f(x)=log2(x+4), what is f^-1(3)?

Sagot :

[tex]f\left( x \right) =\log _{ 2 }{ \left( x+4 \right) } \\ \\ \log _{ 2 }{ \left( x+4 \right) } =y\\ \\ { 2 }^{ y }=x+4[/tex]

[tex]\\ \\ x={ 2 }^{ y }-4\\ \\ \therefore \quad { f }^{ -1 }\left( x \right) ={ 2 }^{ x }-4\\ \\ \therefore \quad { f }^{ -1 }\left( 3 \right) ={ 2 }^{ 3 }-4=4[/tex]
MrRoyal

The value of f^-1(3) is 4

What are inverse functions?

The inverse of a function f(x) is the opposite of the function

How to determine the inverse function?

The function f(x) is given as:

[tex]f(x) = log_2(x + 4)[/tex]

Express f(x) as y

[tex]y = log_2(x + 4)[/tex]

Swap the positions of x and y

[tex]x = log_2(y + 4)[/tex]

Express as exponents

[tex]2^x = y + 4[/tex]

Make y the subject

[tex]y = 2^x - 4[/tex]

Express the equations as an inverse function

[tex]f^{-1}(x) = 2^x - 4[/tex]

Substitute 3 for x in the above equation

[tex]f^{-1}(3) = 2^3 - 4[/tex]

Evaluate

[tex]f^{-1}(3) = 4[/tex]

Hence, the value of f^-1(3) is 4

Read more about inverse functions at:

https://brainly.com/question/14391067

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