Algebra: How to prove functions are injective, surjective and bijective

Math1141. Tutorial 1, Question 3. Examples on how to prove functions are injective.

[sanjaym]

this really helped me a lot for my exam which is tmr, loved your explanation

[Acesif]

Thank you so much, this tutorial is the most helpful of all the other videos I came across

[datawkwardweeb]

This was hella useful lmao
Have a test next week
Thank you so much

[crimson]

20:53 where did you get the "divided by a-5" from? x (5 - a) = -1 - 2 a, so x = (-1 - 2a) / (5-a)

[kimun]

Thanks this by far the clearest video, def subscribing

[mariiooP]

Great examples and excellent explanation. Thanks!

[thefxbro]

in the last proof example why did u divide by a-5 instead of 5-a?

[Shortieauthor]

I thought that when we have absolute value, the results will be always positive. So if we put -1 inside the absolute value, the results will be 1. So i got confuse in the question no. 4, i thought it was injective haha. Please correct me if i'm wrong😊

[JPL]

Proving that a linear transformation is bijective seens so much easier than proving that a normal function like y=x+3 is bijective for some reason

[aayishaabusalih]

Thank you got a better understanding of this concept 👍

[Mariam.Jawabreh]

This video deserves millions of views 🔥🤍🤍🤍, thank you so much

[jubytr]

This is what I was looking for.Thnx .Very well explained.

[radhwanalbedany]

for the question 3 / the function is surjective since its already written that R - {2} this is read as " for all R numbers except number 2"

[janahabachy]

i do not understand why or how did you divide by a-5 at 20:50

[coastcoastpod]

I think by modulus you meant absolute value, but the overall content is understood, thank you.

[jazzysocksdude]

How would this work for functions with multiple expressions, such as f(x) = { x + 1 if x is even, x - 3 if x is odd } ?

[dv]

Why did you add 10 and subtract 10 in the last question?

[stevencheng]

for the second example, shouldn't |x| > 0 but not >= due to natural number? Im still very confused on this topic I hope you could clear my confusion.. thanksss

[elizabethkandjumbi]

At 17:07 where did the 10s come from?

[thefxbro]

(i) Prove that the function f : [1, ∞) −→ [2, ∞) given by f(x) = (x + 2)
is not surjective.(please help)