Question
The function \( f \) is defined by \( f(x)=\frac{4 x-6}{x+7} \). Find \( f(y+4) \). \( f(y+4)=\square \)
Ask by Vargas Ball. in the United States
Feb 19,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( f(y + 4) = \frac{4y + 10}{y + 11} \)
Solution
To find f(y + 4), substitute x = y + 4 into f(x):
f(y + 4) = [4(y + 4) – 6] / [(y + 4) + 7]
Simplify the numerator:
4(y + 4) – 6 = 4y + 16 – 6 = 4y + 10
Simplify the denominator:
(y + 4) + 7 = y + 11
So,
f(y + 4) = (4y + 10) / (y + 11)
Thus, f(y + 4) = (4y + 10) / (y + 11).
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Simplify this solution Extra Insights
To find \( f(y+4) \), we substitute \( y+4 \) into the function \( f(x) \). Starting with the function: \[ f(x) = \frac{4x - 6}{x + 7} \] we replace \( x \) with \( y + 4 \): \[ f(y + 4) = \frac{4(y + 4) - 6}{(y + 4) + 7} \] Now, calculate the numerator: \[ 4(y + 4) - 6 = 4y + 16 - 6 = 4y + 10 \] Next, calculate the denominator: \[ (y + 4) + 7 = y + 11 \] Putting it all together, we have: \[ f(y + 4) = \frac{4y + 10}{y + 11} \] So, \( f(y+4) = \frac{4y + 10}{y + 11} \).
