Find the points of intersection, if any, of the graphs of y = f (x) and y = 4.

Question

Let(x)=4x^2/x^2-1 and g(x)=e^2x^2-1.

 

 

a)    Solve for x the equation

b)    Find the points of intersection, if any, of the graphs of  y = f (x) and y = 4.

c)     Describe the domains of  f (x) and g(x). 

Answer 1

Assuming f(x)=4x^2/(x^2-1) and g(x)=e^(2x^2-1):

a) No specific equation has been given, so there is nothing to solve. f(x)=0 has solution x=0; g(x)=0 has no solution; f(x)=g(x) has no solution.

b) When y=f(x)=4=4x^2/(x^2-1), x^2=x^2-1, or 0=-1 which is false, so there is no intersection between y=4 and y=f(x).

c) Domains: f(x), all x except x=1 or -1, when f(x) tends to infinity; g(x) is defined for all x.

Answer 2

Given f(x)=4x^2/(x^2-1) and g(x)=e^(2x^2-1)

f(x)=g(x)

4x^2/(x^2-1)=e^(2x^2-1)

There is no solution

y=f(x)=4=4x^2/(x^2-1)

x^2=x^2-1

or 0=-1

Hence there is no intersection point

y=f(x)=4=4x^2/(x^2-1), x^2=x^2-1, or 0=-1 which is false, so there is no intersection between y=4 and y=f(x)

Algebra Homework Help