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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

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\( f(y + 4) = \frac{4y + 10}{y + 11} \)

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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, \( f(y+4) = \frac{4y + 10}{y + 11} \).

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