1. 11. Which input produces an oufput of \( f(x)=7 \) for \( f(x)=2 z-3 \) ? \( x=8 \) \( z=0 \) \( z=5 \) \( z=11 \)
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Bonus Knowledge
To find the input that produces an output of \( f(x) = 7 \) for the function \( f(x) = 2z - 3 \), you can set up the equation: \( 2z - 3 = 7 \). Solving this gives \( 2z = 10 \), so \( z = 5 \). Therefore, the input that produces the output of \( f(x) = 7 \) is \( z = 5 \)! Using algebra effectively is like being a magician—you're revealing the secrets hidden within numbers! So, next time you face a function, remember that a little rearranging can unlock the answers you seek. When working on problems like this, one common mistake is forgetting to isolate the variable properly. Always double-check your steps! It's easy to make a quick arithmetic mistake or overlook a negative sign, which can lead you astray. Always keep an eye on the conditions given and follow the problem through to the end.