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Find the following values of the function $\newline$ $\begin{cases} f(x) = \begin{cases} x+2, & x \leq 5 \ 6-x, & x > 5 \end{cases} \end{cases}$ , $f(2)=\square$ , $f(5)=$ , $f(11)=\square$

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Find derivatives of logarithmic functions

Full solution

Q. Find the following values of the function

\newline

\begin{cases} f(x) = \begin{cases} x+2, & x \leq 5 \ 6-x, & x > 5 \end{cases} \end{cases}

,

f(2)=\square

,

f(5)=

,

f(11)=\square

Calculate $f(2)$ : Step $1$ : Determine $f(2)$ using the piecewise function. $\newline$ Since $2 \leq 5$ , use the first part of the function: $f(x) = x + 2$ . $\newline$ Calculation: $f(2) = 2 + 2 = 4$ .
Calculate $f(5)$ : Step $2$ : Determine $f(5)$ using the piecewise function. $\newline$ Since $5 \leq 5$ , use the first part of the function: $f(x) = x + 2$ . $\newline$ Calculation: $f(5) = 5 + 2 = 7$ .
Calculate $f(11)$ : Step $3$ : Determine $f(11)$ using the piecewise function. $\newline$ Since $11 > 5$ , use the second part of the function: $f(x) = 6 - x$ . $\newline$ Calculation: $f(11) = 6 - 11 = -5$ .

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