If [tex]f(x)=3 x+\frac{5}{x}[/tex], what is [tex]f(a+2)[/tex]?
A. [tex]3(a+2)+\frac{5}{a+2}[/tex]
B. [tex]3 a+\frac{5}{a}+2[/tex]
C. [tex]3(f(a))+\frac{5}{f(a)+2}[/tex]
Answer (1)
Substitute a + 2 for x in the function f ( x ) = 3 x + x 5 .
Obtain f ( a + 2 ) = 3 ( a + 2 ) + a + 2 5 .
Compare the result with the given options.
The correct answer is 3 ( a + 2 ) + a + 2 5 .
Explanation
Understanding the problem We are given the function f ( x ) = 3 x + x 5 and we need to find f ( a + 2 ) . This means we need to substitute a + 2 for x in the function's expression.
Substitution Substitute x = a + 2 into the function: f ( a + 2 ) = 3 ( a + 2 ) + a + 2 5 This is a direct substitution, replacing every instance of x with ( a + 2 ) .
Comparison with options Now, let's compare our result with the given options: Option A: 3 ( a + 2 ) + a + 2 5 Option B: 3 a + a 5 + 2 Option C: 3 ( f ( a )) + f ( a ) + 2 5 Our result matches option A exactly.
Final Answer Therefore, f ( a + 2 ) = 3 ( a + 2 ) + a + 2 5 .
Examples
Imagine you are designing a rectangular garden where the length is 'a+2' meters. The function f(x) = 3x + 5/x could represent the amount of fencing needed, where 'x' is the length of one side. Finding f(a+2) helps you calculate the fencing required when the length is 'a+2' meters. This kind of substitution is useful in various real-world scenarios, such as calculating costs, areas, or other quantities that depend on a variable that changes.
