Calculus---Continuity

[mathbaby]

Suppose that f and g are two functions both continuous on the interval [a,b], and such that f(a)=g(b)=p and f(b)=g(a)=q where p is not equal to q. Sketch typical graphs of two functions. Then apply the intermediate value theorem to the function h(x)= f(x)-g(x) to show that f(c)=g(c) at some point c of (a,b)

 

[Deleted member 4993]

Suppose that f and g are two functions both continuous on the interval [a,b], and such that f(a)=g(b)=p and f(b)=g(a)=q where p is not equal to q. Sketch typical graphs of two functions. Then apply the intermediate value theorem to the function h(x)= f(x)-g(x) to show that f(c)=g(c) at some point c of (a,b)

Please share your work with us .

If you are stuck at the beginning tell us and we'll start with the definitions such as "what is intermediate value theorem?"

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/th...217#post322217

 

[HallsofIvy]

Have you noticed that the values of f and g swap at a and b? You are not told which of p and q is larger, only that they are not equal. So do this in two cases: case 1, p< q; case 2, p> q.