Mastering Inverse Functions: Exponential and Logarithmic Forms Explained

the inverse of the exponential function, given as f(x)=logax

logarithmic function

The inverse of the exponential function f(x) = ax is given as g(x) = loga(x).

To find the inverse of f(x) = loga(x), we can switch x and y in the equation and solve for y:

x = loga(y)

Rewrite this in exponential form:

a^x = y

Therefore, the inverse of f(x) = loga(x) is:

g(x) = a^x

Therefore, we can say:

f(g(x)) = loga(a^x) = x

g(f(x)) = a^(loga(x)) = x

This shows that f(x) and g(x) are inverse functions of each other.

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