Question

The inverse of the logarithmic function f(x) = log0. 5x is f−1(x) = 0. 5x. What values of a, b, and c complete the table for the inverse function?.

Answer 1

The values of a, b, and c to complete the table for the inverse of the logarithmic function is 2,1 and -2 respectively.

What is the inverse of the logarithmic function?

The Inverse of the logarithmic function is an exponential function.

The given logarithmic function is,

$f(x) = \log_{0. 5}x$

The inverse of the given logarithmic function is,

$f^{-1}(x) = 0.5^x.$

Put the value of x as -1 from the table attached below, to find the value of a.

$f^{-1}(-1) = 0.5^{(-1)}\\f^{-1}(-1) = 2$

Similarly, put the value of x as 0 from the table attached below, to find the value of b.

$f^{-1}(0) = 0.5^{(0)}\\f^{-1}(0) = 1$

Now, put the value of x as 2 from the table attached below, to find the value of c.

$f^{-1}(2) = 0.5^{(2)}\\f^{-1}(2) = -2$

Thus, the values of a, b, and c to complete the table for the inverse of the logarithmic function is 2,1 and -2 respectively.

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