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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