Question

If f(x)=1/x+2 what is f(3+h)

Answer 1

Let x = 3+h
$\frac{1}{(3 + h) + 2} \\ = \frac{1}{h + 3 + 2} \\ = \frac{1}{h + 5}$
The answer is A.

Answer 2

Answer: A. $\dfrac{1}{h+5}$

Step-by-step explanation:

The given function: $f(x)=\dfrac{1}{x+2}$

To find the value of $f(3+h)$, we need to  replace 'x' by (3+h) , we get

$f(3+h)=\dfrac{1}{3+h+2}\\\\\Rightarrow\ f(3+h)=\dfrac{1}{3+2+h} .........................\text{[By commutative property ]}\\\\\Rightarrow\ f(3+h)=\dfrac{1}{5+h}\\\\\Rightarrow\ f(3+h)=\dfrac{1}{h+5}$

Hence, the value of $f(3+h)=\dfrac{1}{h+5}$