Consider f: R+ -> [-9,infinity] given by f(x) = 5x^(2) + 6x - 9. Prove that f in invertible and the inverse is [54+5y]^(1/2) - / 5
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f: R+ → [−5, ∞) given by f(x) = 9x2 + 6x − 5
to show that function is one-one. we will show it by the contradiction.
let us take function is not one-one. therefore there exist two or more numbers for which images are same.
we will take two different numbers 
let 

since  are positive. therefore  it cannot be zero.
therefore 
therefore it contradicts our assumption. hence the function is one-one.
A function f:X→Y is onto if for every y∈Y there exist a preimage in X.
let y= 9x2 + 6x − 5


hence f(x)=y therefore f(x) is onto.
to show that function is one-one. we will show it by the contradiction.
let us take function is not one-one. therefore there exist two or more numbers for which images are same.
we will take two different numbers 
let 

since  are positive. therefore  it cannot be zero.
therefore 
therefore it contradicts our assumption. hence the function is one-one.
A function f:X→Y is onto if for every y∈Y there exist a preimage in X.
let y= 9x2 + 6x − 5


hence f(x)=y therefore f(x) is onto.
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