[tex]f(x)=3(x+5)+\dfrac{4}{x}\\\\f(a+2)\to\text{put x = a + 2 to the equation of the function f}\\\\f(a+2)=3(a+2+5)+\dfrac{4}{a+2}=3(a+7)+\dfrac{4}{a+2}[/tex]
Answer:
The value of [tex]f(a+2)[/tex] is [tex]3a+21+\frac{4}{a+2}[/tex].
Step-by-step explanation:
Consider the provided function [tex]f(x)=3(x+5)+\frac{4}{x}[/tex]
In order to find the value of [tex]f(a+2)[/tex]
Substitute x = a + 2 in the provided function.
[tex]f(a+2)=3((a+2)+5)+\frac{4}{a+2}[/tex]
[tex]f(a+2)=3(a+2+5)+\frac{4}{a+2}[/tex]
[tex]f(a+2)=3(a+7)+\frac{4}{a+2}[/tex]
Now, apply the distributive property: [tex]a(b+c)=ab+ac[/tex]
[tex]f(a+2)=3a+21+\frac{4}{a+2}[/tex]
Therefore, the value of [tex]f(a+2)[/tex] is [tex]3a+21+\frac{4}{a+2}[/tex].
