Questions: Evaluate f(a+h) if f(x) = (6x-1)/(5x+1)

Evaluate f(a+h) if f(x) = (6x-1)/(5x+1)
Transcript text: Evaluate $f(a+h)$ if $f(x)=\frac{6 x-1}{5 x+1}$
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Solution

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Solution Steps

To evaluate \( f(a+h) \) for the function \( f(x) = \frac{6x - 1}{5x + 1} \), substitute \( a+h \) into the function in place of \( x \). This involves replacing every instance of \( x \) in the function with \( a+h \).

Step 1: Substitute \( a+h \) into the Function

To evaluate \( f(a+h) \) for the function \( f(x) = \frac{6x - 1}{5x + 1} \), substitute \( a+h \) in place of \( x \). This gives:

\[ f(a+h) = \frac{6(a+h) - 1}{5(a+h) + 1} \]

Step 2: Simplify the Expression

Expand and simplify the expression:

\[ f(a+h) = \frac{6a + 6h - 1}{5a + 5h + 1} \]

Final Answer

The expression for \( f(a+h) \) is:

\[ \boxed{\frac{6a + 6h - 1}{5a + 5h + 1}} \]

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