Answer
g(0) = 5
g(-4 ) = -3
g(-7) = -9
g(8) = 21
g(a+2) = 2a+9
g(a)+2 = 2a+7
Work Step by Step
The problem is asking for us to find the function values. the function is
$g(x)=2x+5$
In order to solve for g, we just replace x with g(x).
(a) $g(0)$
Part (a) is telling us to replace x with 0.
$g(0)=2(0) + 5$
$g(0)=0+5$
$g(0)=5$
Part (b) wants us to replace x with -4.
(b) $g(-4)$
$g(-4)=2(-4)+5$
$g(-4)=-8+5$
$g(-4)=-3$
Problem (c) asks use to replace x with -7
(c) $g(-7)$
$g(-7)=2(-7)+5$
$g(-7)=-14+5$
$g(-7)=-9$
Problem (d) asks for us to replace x with 8
(d) $g(8)$
$g(8)=2(8)+5$
$g(8)=16+5$
$g(8)=21$
Problem (e) asks for x to equal (a+2)
(e)$g(a+2)$
$g(a+2)=2(a+2)+5$
This problem is different from our previous ones. The other problems required for use to multiply two numbers. This problem, instead has us distribute 2.
$g(a+2)=2a+4+5$
You now add all numbers that can be added. 2a cannot be added with the other numbers since it has a variable.
$g(a+2)=2a+9$
Part (f) tells us x equals (a) +2.
(f) $g(a)+2$
This problem looks similar to part (e). However, there are asking for different things.
$g(a)+2) =2(a)+2+5$
In the other problem, you distributed the 2 amongst(a+2). In this problem, however, only a is in the parenthesis. This means only a is multiplied by the number 2. The two parenthesis signify that the equation replaces x, but only a is multiplies by 2, Because of this the next part should look like this.
g((a)+2)= 2a+2+5
g((a)+2)= 2a+7
This is your answer for part (f).
