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Math  /  Algebra

Questionf(x)={x+24<x<5x+35⩽x<6f(5)=\begin{array}{l}f(x)=\left\{\begin{array}{ll}x+2 & 4<x<5 \\ x+3 & 5 \leqslant x<6\end{array}\right. \\ f(5)=\end{array}

Studdy Solution

STEP 1

1. We are given a piecewise function f(x) f(x) .
2. The function has two pieces: - f(x)=x+2 f(x) = x + 2 for 4<x<5 4 < x < 5 - f(x)=x+3 f(x) = x + 3 for 5≤x<6 5 \leq x < 6
3. We need to find the value of f(5) f(5) .

STEP 2

1. Identify the correct piece of the piecewise function for x=5 x = 5 .
2. Substitute x=5 x = 5 into the appropriate piece of the function.
3. Simplify the expression to find f(5) f(5) .

STEP 3

Determine which piece of the piecewise function applies when x=5 x = 5 .
- The first piece x+2 x + 2 is valid for 4<x<5 4 < x < 5 , which does not include x=5 x = 5 . - The second piece x+3 x + 3 is valid for 5≤x<6 5 \leq x < 6 , which includes x=5 x = 5 .
Thus, we use the second piece of the function.

STEP 4

Substitute x=5 x = 5 into the second piece of the function:
f(5)=5+3 f(5) = 5 + 3

STEP 5

Simplify the expression:
f(5)=8 f(5) = 8
The value of f(5) f(5) is:
8 \boxed{8}

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