Question Find $g(a+1)$ when $g(x) = \frac{1}{2} x + 5$ .

Studdy Solution

STEP 1

Assumptions
1. The function given is $g(x) = \frac{1}{2} x + 5$ .
2. We need to find the value of $g(a+1)$ .

STEP 2

To find $g(a+1)$ , we will substitute $x$ with $a+1$ in the function $g(x)$ .
$g(a+1) = \frac{1}{2} (a+1) + 5$

STEP 3

Distribute the $\frac{1}{2}$ across the terms inside the parentheses.
$g(a+1) = \frac{1}{2} \cdot a + \frac{1}{2} \cdot 1 + 5$

STEP 4

Simplify the expression by performing the multiplication.
$g(a+1) = \frac{1}{2} a + \frac{1}{2} + 5$

STEP 5

Combine the constant terms $\frac{1}{2}$ and $5$ .
$g(a+1) = \frac{1}{2} a + \frac{10}{2} + \frac{1}{2}$

STEP 6

Add the fractions $\frac{10}{2}$ and $\frac{1}{2}$ .
$g(a+1) = \frac{1}{2} a + \frac{11}{2}$
The value of $g(a+1)$ is $\frac{1}{2} a + \frac{11}{2}$ .

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