Question

If ( f(x) = frac{√{x-3}}{x+2} ), complete the following statement: What is ( f(9) )?

Answer 1

If ( f(x) = frac{√{x-3}}{x+2} ),
`\( f(9) = (√(6))/(11) \).`

Step-by-step explanation:

The given function is
`\( f(x) = (√(x-3))/(x+2) \).` To find
`\( f(9) \),` substitute
`\( x = 9 \)` into the function.

`\[ f(9) = (√(9-3))/(9+2) = (√(6))/(11) \].`

In the numerator,
`\( √(9-3) \)` simplifies to
`\( √(6) \),` and in the denominator,
`\( 9+2 \)`simplifies to
`\( 11 \).` Therefore,
`\( f(9) \) is \( (√(6))/(11) \).`

This result implies that when
`\( x = 9 \),` the function
`\( f(x) \)` evaluates to
`\( (√(6))/(11) \).` The square root in the numerator signifies that the value inside the radical,
`\( x-3 \),` contributes to the final result. The denominator,
`\( x+2 \)` , determines the fraction's overall scale. Thus,
`\( f(9) \)` is a rational expression involving the square root of 6, reflecting the function's behavior at
`\( x = 9 \).`

In summary, the calculation involves straightforward substitution into the given function, demonstrating how
`\( f(x) \)` behaves at the specific point
`\( x = 9 \).` The result
`\( (√(6))/(11) \)` provides a precise representation of the function's output at this particular input.