Determine whether each of these functions is a bijection from R to R. <br> <math xmlns="http://www.w3.org/1998/Math/MathML"> <mi>f</mi> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> <mo>=</mo> <mo>&#x2212;<!-- − --></mo> <mn>3</mn> <mi>x</mi> <mo>+</mo> <mn>4</mn> </math>

Moncelliqo4

Moncelliqo4

Answered question

2022-11-28

Determine whether each of these functions is a bijection from R to R.

Answer & Explanation

Maryjane Estrada

Maryjane Estrada

Beginner2022-11-29Added 10 answers

Let us consider if there exist two such elements. Suppose f ( x ) = f ( y ). Then 3 x + 4 = 3 y + 4, which implies x = y. So here we've get an implication: " f ( x ) = f ( y ) " " x = y " .
For the onto-ness, we check if all elements in the codomain, namely R , are all been mapped. We start the argument:
For each y R , is there an x R , such that f ( x ) = y ?

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