Which function has an inverse function?
2 answers:
Answer:
The correct option is 2.
Step-by-step explanation:
A function has an inverse function if and only if it is a one-to-one function. It means for each value of x there exist a unique value of y.
In option 1,
It is an absolute function. For each value of x there axis more than 1 value of f(x). Therefore this function does not has an inverse function.
In option 2,
The degree of the function is 5 which is an odd number. Therefore it is a one-to-one function. Therefore this function has an inverse function.
In option 3,
The degree of the function is 4 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.
In option 4,
The degree of the function is 2 which is an even number. Therefore it is not a one-to-one function. Therefore this function does not has an inverse function.
Hence option 2 is correct.
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Answer:
A two column proof is presented as follows;
Statement Reason
1. AB ║ DE, BD bisects AE Given
2. ∠BAE = ∠AED, ∠ABD = ∠BDA Alternate ∠s are equal
3. =
,
=
By definition of bisection of line AE by BD
4. ΔABC ≅ ΔEDC By SAA, rule of congruency
Step-by-step explanation:
Step 1. AB ║ DE, BD bisects AE Given
Step 2. ∠BAE , ∠AED, and ∠ABD, ∠BDA are pairs of alternate angles formed by the parallel lines, AB and DE and are therefore, equal
Step 3. =
,
=
The bisection of line gives two lines of equal length. The bisection of AE by BD gives,
and
where
=
Similarly, the bisection of BD by AE gives, and
, where
=
Step 4. ΔABC ≅ ΔEDC By the Side-Angle-Angle (SAA), rule of congruency, which states that two triangles having two angles and the corresponding non included sides of each triangle equal to the other, the two triangles are congruent.