use functions ( f(x)=x^{2}-100 ) and ( g(x)=-x^{2}+100 ) to answer the questions.\n(a) solve ( f(x)=0…

use functions ( f(x)=x^{2}-100 ) and ( g(x)=-x^{2}+100 ) to answer the questions.\n(a) solve ( f(x)=0 ).\n(d) solve ( f(x)>0 ).\n(g) solve ( f(x) geq 1 ).\n(b) solve ( g(x)=0 ).\n(e) solve ( g(x) leq 0 ).\n(c) solve ( f(x)=g(x) ).\n(f) solve ( f(x)>g(x) ).\n(b) the solution set is ( {-10,10} ).\n(type an integer or a fraction. use a comma to separate answers as needed.)\n(c) the solution set is ( {-10,10} ).\n(type an integer or a fraction. use a comma to separate answers as needed.)\n(d) solve ( f(x)>0 ). select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the solution set is ( (-infty,-10) cup(10, infty) ).\n(type your answer in interval notation. simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for\nany numbers in the expression.)\nb. the solution set is the empty set.\n(e) solve ( g(x) leq 0 ). select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the solution set is\n(type your answer in interval notation. simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for\nany numbers in the expression.)\nb. the solution set is the empty set.

use functions ( f(x)=x^{2}-100 ) and ( g(x)=-x^{2}+100 ) to answer the questions.\n(a) solve ( f(x)=0 ).\n(d) solve ( f(x)>0 ).\n(g) solve ( f(x) geq 1 ).\n(b) solve ( g(x)=0 ).\n(e) solve ( g(x) leq 0 ).\n(c) solve ( f(x)=g(x) ).\n(f) solve ( f(x)>g(x) ).\n(b) the solution set is ( {-10,10} ).\n(type an integer or a fraction. use a comma to separate answers as needed.)\n(c) the solution set is ( {-10,10} ).\n(type an integer or a fraction. use a comma to separate answers as needed.)\n(d) solve ( f(x)>0 ). select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the solution set is ( (-infty,-10) cup(10, infty) ).\n(type your answer in interval notation. simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for\nany numbers in the expression.)\nb. the solution set is the empty set.\n(e) solve ( g(x) leq 0 ). select the correct choice and, if necessary, fill in the answer box to complete your choice.\na. the solution set is\n(type your answer in interval notation. simplify your answer. type an exact answer, using radicals as needed. use integers or fractions for\nany numbers in the expression.)\nb. the solution set is the empty set.

Answer

Explanation:

Step1: Solve the inequality (g(x)\leq0)

Given (g(x)=-x^{2}+100), set up the inequality (-x^{2}+100\leq0). First, rewrite it as (x^{2}-100\geq0) (by multiplying both sides by (- 1) and reversing the inequality sign). Factor the left - hand side: (x^{2}-100=(x - 10)(x + 10)\geq0).

Step2: Find the critical points

Set ((x - 10)(x + 10)=0). The critical points are (x=-10) and (x = 10).

Step3: Test intervals

  • For (x<-10), let (x=-11). Then ((-11 - 10)(-11 + 10)=(-21)\times(-1)=21>0).
  • For (-10<x<10), let (x = 0). Then ((0 - 10)(0 + 10)=(-10)\times(10)=-100<0).
  • For (x>10), let (x = 11). Then ((11 - 10)(11 + 10)=(1)\times(21)=21>0).

Answer:

A. The solution set is ((-\infty,-10]\cup[10,\infty))