Question

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

Answer 1

If x is the only thing in the denominator, then,

$f(x) = \frac{1}{x}+2\\\\f(3+h) = \frac{1}{3+h}+2\\\\f(3+h) = \frac{1}{3+h}+2\left(\frac{3+h}{3+h}\right)\\\\f(3+h) = \frac{1+2(3+h)}{3+h}\\\\f(3+h) = \frac{1+6+2h}{3+h}\\\\f(3+h) = \frac{7+2h}{3+h}$

We replace every copy of x with 3+h, as shown in the second step. Afterwards, we can optionally simplify to form one big fraction.

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Or if the "x+2" is in the denominator, then we have these steps:

$f(x) = \frac{1}{x+2}\\\\f(3+h) = \frac{1}{3+h+2}\\\\f(3+h) = \frac{1}{h+5}$