$x=-2 \lor$.
Step 4: Evaluate the function at two other $x$-values:
$h(-4)=-2 \lor h(-6)=$
$\square$
Answer (2)
We are given x = − 2 v and h ( x ) = − 2 v .
Express v in terms of x : v = − 2 x .
Substitute v into h ( x ) : h ( x ) = − 2 ( − 2 x ) = x .
Evaluate h ( − 4 ) and h ( − 6 ) : h ( − 4 ) = − 4 and h ( − 6 ) = − 6 .
The final answer is − 4 , − 6 .
Explanation
Expressing h(x) in terms of x We are given that x = − 2 v and we need to evaluate the function h ( x ) = − 2 v at x = − 4 and x = − 6 . The key is to express h ( x ) in terms of x only. Since x = − 2 v , we can solve for v in terms of x by dividing both sides by − 2 , which gives us v = − 2 x . Now we can substitute this expression for v into the function h ( x ) = − 2 v .
Simplifying h(x) Substituting v = − 2 x into h ( x ) = − 2 v , we get h ( x ) = − 2 ( − 2 x ) = x . So, h ( x ) = x . This means that the value of the function h at any value of x is simply equal to that value of x .
Evaluating h(-4) and h(-6) Now we can evaluate h ( − 4 ) and h ( − 6 ) .
For x = − 4 , we have h ( − 4 ) = − 4 .
For x = − 6 , we have h ( − 6 ) = − 6 .
Final Answer Therefore, h ( − 4 ) = − 4 and h ( − 6 ) = − 6 .
Examples
Understanding functions and variable substitution is crucial in many real-world applications. For example, in physics, you might have a formula that relates the position of an object to time, but you need to express it in terms of velocity. By substituting the relationship between time and velocity, you can rewrite the formula to directly calculate the position based on the object's velocity. This is similar to what we did in this problem, where we rewrote the function in terms of a different variable to make it easier to evaluate.
The function h ( x ) simplifies to h ( x ) = x , so evaluating it at x = − 4 gives h ( − 4 ) = − 4 , and at x = − 6 gives $h(-6) = -6.
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