Part A:
The solution of the equations p(x) and g(x) is the intersection of the two lines.
p(x): y=3x-15..................(1)
g(x): y=-2x+5..................(2)
By comparison, 3x-15=-2x+5 => 5x=20 => x=4
Substitute x=4 in (1), y=3(4)-15=12-15=-3
=> Solution: (4,-3)
(see second attached image)
Part B: write any two solutions for g(x).
We cannot write a solution to a function unless there is an equation.
ASSUMING what is meant is to write two points that lie on the line g(x), then we can assume any two values of x, say x1, x2, and evaluate y1=g(x1) and y2=g(x2).
If x1=0, then g(x1)=g(0)=-2(0)+5=5 => point is (0,5)
If x2=1, then g(x2)=g(1)=-2(1)+5=-2+5=3 => point is (1,3) .... and so on.
Part C: what is the solution to the equation g(x)=f(x)
g(x)=f(x) => -2x+5=4+1.5^x => 1.5^x+2x-1=0 .......................(3)
There is no analytic solution to solve this kind of problems. However, we can always solve it graphically and check the answer algebraically.
As we can see from the third graph, the solution is (0,5).
Check: 1.5^(0)+2(0)-1 = 1+0-1 = 0 => solution (0,5) is good.
Answer: solution is (0,5)
The solution of the equations p(x) and g(x) is the intersection of the two lines.
p(x): y=3x-15..................(1)
g(x): y=-2x+5..................(2)
By comparison, 3x-15=-2x+5 => 5x=20 => x=4
Substitute x=4 in (1), y=3(4)-15=12-15=-3
=> Solution: (4,-3)
(see second attached image)
Part B: write any two solutions for g(x).
We cannot write a solution to a function unless there is an equation.
ASSUMING what is meant is to write two points that lie on the line g(x), then we can assume any two values of x, say x1, x2, and evaluate y1=g(x1) and y2=g(x2).
If x1=0, then g(x1)=g(0)=-2(0)+5=5 => point is (0,5)
If x2=1, then g(x2)=g(1)=-2(1)+5=-2+5=3 => point is (1,3) .... and so on.
Part C: what is the solution to the equation g(x)=f(x)
g(x)=f(x) => -2x+5=4+1.5^x => 1.5^x+2x-1=0 .......................(3)
There is no analytic solution to solve this kind of problems. However, we can always solve it graphically and check the answer algebraically.
As we can see from the third graph, the solution is (0,5).
Check: 1.5^(0)+2(0)-1 = 1+0-1 = 0 => solution (0,5) is good.
Answer: solution is (0,5)