How can the inverse relationship between an exponential function and its inverse logarithmic function be explained?

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The inverse of the exponential function f(x)=2x−3 is . While the graph of the exponential function is a shift of 3 units Response area from its parent function, the logarithmic function is a shift of 3 units Response area from its parent function.

The inverse of the exponential function f(x)=2x−3 is [tex]y = \log_{2}{x + 2}[/tex]. While the graph of the exponential function is a shift of 3 units down from it's parent function, the logarithmic function is a shift of 3 units left from it's parent function.

Exponential and logarithmic functions

The exponential function in this problem is given as follows:

[tex]y = 2^x - 3[/tex]

Which is a shift down of 3 units from the parent function [tex]y = 2^x[/tex], due to the subtraction by 3.

To find the inverse function, x and y are exchanged, and then y is isolated, as follows:

[tex]x = 2^y - 3[/tex]

[tex]2^y = x + 3[/tex]

[tex]\log_{2}{2^y} = \log_{2}{x + 3}[/tex]

[tex]y = \log_{2}{x + 3}[/tex]

Which is a shift of 3 units left of the parent function [tex]y = \log_{2}{x}[/tex], due to the addition of 3 on the domain x.

More can be learned about inverse functions at https://brainly.com/question/11735394

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