The graph of f(x) is shown below. where is f(x) < 0? write your answer in interval notation.

The graph of  f(x) passes through (1,1) , (2,1.4...), (3,1.7),(4,2)

As, this curve is not linear.

To find the graph of a inverse function if a function is given

As we can see that ,

√1=1

√2=1.414..

√3=1.732..

√4=2

it means, √x=y is f(x).

So, to find the inverse of f(x), follow the procedure

Squaring both sides

Replace x by y and y by x to get inverse of f(x)

So,there will be two inverses of f(x)

1. x=√y

2. x= -√y

Domain of g(x)∈[0,∞], means y≥0.

Option A, 2nd graph below. and Option B. 3 rd Graph below is true regarding graph of g(x).

not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this