Answer:
[tex](-4,-13)[/tex] and [tex](4,3)[/tex] the intersection points.
Step-by-step explanation:
Intersection point of two functions is a common point which satisfies both the functions.
Given functions are,
[tex]f(x)=2x-5[/tex]
[tex]g(x)=x^2+2x-21[/tex]
For a common point of these functions,
[tex]f(x)=g(x)[/tex]
[tex]2x-5=x^2+2x-21[/tex]
[tex]-5=x^2-21[/tex]
[tex]0=x^2-16[/tex]
[tex]x^2=16[/tex]
[tex]x=-4,4[/tex]
For [tex]x=-4[/tex],
[tex]f(-4)=g(-4)=2(-4)-5[/tex]
[tex]=-13[/tex]
For [tex]x=4[/tex],
[tex]f(4)=g(4)=2(4)-5[/tex]
[tex]=3[/tex]
Therefore, [tex](-4,-13)[/tex] and [tex](4,3)[/tex] the intersection points.
