CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Let f and g be two differentiable functions such that f(x)=ϕ(x) and ϕ(x)=f(x) for all real x. If f(3)=5 and f(3)=4, then the value of (f(10))2(ϕ(10))2 is 


Solution

 Let h(x)=(f(x))2(ϕ(x))2
h(x)=2f(x)f(x)2ϕ(x)ϕ(x)
h(x)=2f(x)f(x)2f(x)f(x)
   (f(x)=ϕ(x), ϕ(x)=f(x))
h(x)=0  xR
h(x) is a constant function. 
h(10)=h(3)
              =(f(3))2(ϕ(3))2
              =(f(3))2(f(3))2
              =5242=9

Mathematics

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image