Video Transcript
Consider the function 𝑓 of 𝑥
equals negative three times the square root of 𝑥 plus two minus one. The function 𝑔 of 𝑥 is obtained
by reflecting the graph of 𝑓 of 𝑥 in the 𝑦-axis. What is the equation of 𝑔 of
𝑥?
We’re asked to write the equation
of 𝑔 of 𝑥, which is the reflection of 𝑓 of 𝑥 in the 𝑦-axis. To proceed, we will need to recall
the definition of a function reflection in the 𝑦-axis.
If we consider a function 𝑦 equals
𝑓 of 𝑥, a reflection in the 𝑦-axis can be produced using the function 𝑦 equals
𝑓 of negative 𝑥. This means we can find 𝑔 of 𝑥 by
taking 𝑓 of negative 𝑥. So we substitute negative 𝑥 for 𝑥
in the original function. After simplifying, we have 𝑔 of 𝑥
equals negative three times the square root of two minus 𝑥 minus one.
In conclusion, we found the
equation of the reflection of the 𝑓 of 𝑥 function in the 𝑦-axis by substituting
negative 𝑥 for 𝑥 and simplifying the expression.
