Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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For the function f(x) = b^x, what is its inverse?

f(x) = logb(x)
f(x) = e^x
f(x) = b/x
f(x) = x+b

The correct answer is: f(x) = logb(x)

The function f(x) = b^x represents an exponential function, where b is a positive real number and x is the exponent. To find the inverse of this function, we look for a function that undoes the effect of raising b to the power of x. The correct inverse function is given by f(x) = logb(x), which is the logarithmic function with base b. When you apply the logarithm to b raised to a power, you recover the exponent itself. This means that if y = b^x, then taking the logarithm base b of both sides gives logb(y) = x. This relationship shows that the logarithmic function effectively reverses the operation of exponentiation. In this context, the logarithm provides a way to express the input x in terms of the output y from the exponential function. Therefore, logb(x) serves as the inverse of b^x, confirming that the answer is indeed a valid representation of the mathematical inverse of the function.