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? x −2 −1 0 1 2 y 4 a b 0. 5 c a = b = c =.

Answer 1

The value of a, b and c can be calculated using the inverse function.

The calculated the value of a= 2, b=1 and c= -2.

Given:

The function is  $f(x)=\log_{0.5}x$ and its inverse is $f^{-1}(x)=0.5^x$ .

What is an inverse function?

• The inverse function of a function is defined if $f$ is a function that undoes the operation of $f$.

• The inverse of $f$ exists if and only if $f$ is bijective, and if it exists, is denoted by $f^{-1}$.

Substitute the value of x= -1 in a given inverse function and calculate the value of a.

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

Substitute the value of x  is 0 in given inverse function.

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

Substitute the value of x  is 2 in given inverse function.

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

Therefore, the value of a= 2, b=1 and c=-2.

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