Let `f:[0'1] to [-1,1]` and `g:[-1,1] to [0,2]` be two functions such that g is injective and `g^(@) f:[0,1] to [0,2]` is surjective. Then

Options

A. f must be injective but need not be surjective
B. f must be surjective but need not be injective
C. f must be bijective
D. f must be a constant functions.

Answer

B

Explanation

let h(x)=9(f(x))
and n(x) is onto (given)
`:.` Co-domain of h(x)= Range of h(x)
Range of h(x)=[0,2]
and h(x)= 9(f(x)) it means g is giving [0,2] which is also co-domain of g.
So, g must be onto.
Now, Domain ofg g=[-1,1] which must be range of f.
But,co-domain of f=[-1,1]
So, f must be onto