Which of the following expressions represents the inverse of 4^x?

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Question: Which of the following expressions represents the inverse of 4^x?

Options:

Correct Answer: Both 1/4^x and 4^(-x)

Solution:

Both 1/4^x and 4^(-x) represent the inverse of 4^x.

Which of the following expressions represents the inverse of 4^x?

Which of the following expressions represents the inverse of 4^x?

Step 1: Understand what an inverse means in mathematics. The inverse of a function 'f(x)' is a function that reverses the effect of 'f'.
Step 2: Identify the expression we are working with, which is '4^x'.
Step 3: Recall that the inverse of an exponential function like '4^x' can be represented in two ways: using a negative exponent or a reciprocal.
Step 4: The first way to express the inverse is to use a negative exponent. This means we can write '4^(-x)', which is the same as '1/(4^x)'.
Step 5: The second way to express the inverse is to take the reciprocal of the original expression. This gives us '1/(4^x)'.
Step 6: Conclude that both '4^(-x)' and '1/(4^x)' are valid expressions for the inverse of '4^x'.

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