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Let f(x)=(x)/(x+3), then f(x+1)=?...

Let `f(x)=(x)/(x+3)`, then `f(x+1)=?`

A

`(3x+2)/(x+2)`

B

`(x+1)/(x+4)`

C

`(x+1)/(x+3)`

D

`(2x+3)/(x+3)`

Text Solution

AI Generated Solution

The correct Answer is:
To find \( f(x+1) \) for the function \( f(x) = \frac{x}{x+3} \), we will follow these steps: ### Step 1: Substitute \( x + 1 \) into the function We start with the function: \[ f(x) = \frac{x}{x + 3} \] To find \( f(x + 1) \), we replace \( x \) with \( x + 1 \): \[ f(x + 1) = \frac{x + 1}{(x + 1) + 3} \] ### Step 2: Simplify the denominator Now, simplify the denominator: \[ f(x + 1) = \frac{x + 1}{x + 1 + 3} = \frac{x + 1}{x + 4} \] ### Final Answer Thus, the final result is: \[ f(x + 1) = \frac{x + 1}{x + 4} \] ---
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