Johnston Salinas
09/07/2024 · Primary School
The function \( h \) is defined by \( h(x)=\frac{x+2}{2 x+7} \) Find \( h(3 a) \)
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Tutor-Verified Answer
Step-by-step Solution
To find \( h(3a) \) for the function \( h(x) = \frac{x+2}{2x+7} \), we will substitute \( 3a \) into the function in place of \( x \).
Starting with the function:
\[
h(x) = \frac{x+2}{2x+7}
\]
we substitute \( x = 3a \):
\[
h(3a) = \frac{3a + 2}{2(3a) + 7}
\]
Now, we simplify the expression in the denominator:
\[
2(3a) = 6a
\]
Thus, the denominator becomes:
\[
6a + 7
\]
Now we can write the full expression for \( h(3a) \):
\[
h(3a) = \frac{3a + 2}{6a + 7}
\]
Therefore, the final result is:
\[
\boxed{\frac{3a + 2}{6a + 7}}
\]
Quick Answer
\( h(3a) = \frac{3a + 2}{6a + 7} \)
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