1.

Let f:[0,1] to Rbe an injective continuous function that satisfies the condition -1 lt f(0) lt f(1) lt 1 Then the number of functions g:[-1,1] to [0,1]such that (gof)x =xfor all x in [0,1] is

Answer»

0
1
more than 1, but finite
infinite

Solution :Only condition that g(x) should satisfy for`GOF(x)=x Aax in [0,1]` is that g(x) shold attain all VALUES in [0,1] when RANGE of f(x) s SUBSET of `(-1,1)` is used as image for g(x). Thus there can be infinite such functions g(x) with domain [-1,1] and range [0,1]


Discussion

No Comment Found

Related InterviewSolutions