Which expression is equivalent to (st)(6)?
s(t(6))
s(x) × t(6)
s(6) × t(6)
6 × s(x) × t(x)
The Correct Answer and Explanation is :
To determine which expression is equivalent to ((st)(6)), we first need to clarify what ((st)(6)) means. In this context, (s) and (t) are functions, and the expression ((st)(6)) implies that we are multiplying the results of the functions (s) and (t) evaluated at 6. We can interpret this as:
[
(st)(6) = s(6) \cdot t(6)
]
Now, let’s examine the provided options:
- (s(t(6))): This expression suggests that we first evaluate (t(6)) and then apply the function (s) to that result. This is not equivalent to ((st)(6)) because we are not multiplying the outputs of (s) and (t); instead, we are applying (s) to the output of (t).
- (s(x) \times t(6)): In this expression, (s(x)) implies that we are evaluating the function (s) at some variable (x), while (t(6)) is correctly evaluated at 6. This is not equivalent to ((st)(6)) because (s(x)) does not match the requirement to evaluate (s) at 6.
- (s(6) \times t(6)): This expression directly matches our derived interpretation of ((st)(6)). We are taking the value of (s) evaluated at 6 and multiplying it by the value of (t) also evaluated at 6. Thus, this is equivalent to ((st)(6)).
- (6 \times s(x) \times t(x)): This expression introduces a constant multiplier of 6 and evaluates both (s) and (t) at a variable (x). This is not equivalent to ((st)(6)) as it alters both the inputs and includes an extraneous factor of 6.
Conclusion
The expression that is equivalent to ((st)(6)) is (s(6) \times t(6)). This conclusion is based on understanding that the notation ((st)(6)) signifies the multiplication of two functions evaluated at the same argument, specifically 6, which is accurately represented in the third option.