Solution:
we are given that
we have been asked to find f(x).
we can find the value of f(x) by re-writing the given function in the form of f(x+3) and thereafter we will replace (x+3) by x.
we can re-write the given function as below
Hence the expression representing f(x) is f(x)=4x+3.
Graph the system of linear inequalities
x + y > 5
- x - y < -5
First we graph x + y >5
Step 1: replace > symbol by = sign
x + y =5
step 2 : Solve the equation for y
x + y =5 (subtract x from both sides)
y = 5 - x
step 3: Now we make a table . plug in some number for x and find out y
x -----> y
-1 -----> 6 ( y=5-x => y=5-(-1)= 6)
0 -----> 5 ( y=5-x => y=5-(0)= 5)
1 -----> 4 ( y=5-x => y=5-(1)= 4)
Step 4: we graph the table.
step 5: Shade the region that satisfies our inequality
x + y > 5. Greater than symbol implies that we shade the graph to the right
Graphing second inequality - x - y < -5
All terms have negative sign . so divide all the terms by -1. When we divide an inequality by -1 its sign changes
- x - y < -5 becomes x + y > 5
Follow the same steps to graph this inequality
After dividing the second equation by -1 , we got the same as the first equation.
So we will get the same graph
Both graphs overlaps
The graph of first and second inequality overlaps
The graph is attached below
