Functions Help

[PureConfusion1243]

Hi, I have a homework question about two functions, q(x) = 5x – 1 and j(x) = x2 – 4x + 6, and I don't know how to start answering the questions about them?
a) Show that j(x) > 0 for all values of x.
b) Find the range of j(x).
c) Find any values of x for which elements of the domain are mapped to themselves for j(x).
d) Find the composite function jq(x), simplifying your answer fully

If you could help, that would be great! Thank you xx

 

[ksdhart2]

These problems are mostly just a matter of knowing some definitions and being able to suss out what the problem means.

For (a), think about what you know about the shape of the graph of j(x). What do you know about similar graphs? Specifically, how might you find the minimum value of j(x)? Then think about why that satisfies the criteria that j(x) > 0 for all x.

For (b), refresh yourself on the definition of the domain and range of a function. If you've memorized that definition, the answer to this question follows directly from what you found in part (a).

For (c), consider that "mapped to themselves" means j(x) = x.

For (d), refresh yourself on the definition of composition of functions and then just plug-n-chug.

Now it's your turn to give it your best effort. If you get stuck again, that's quite alright, but when you reply back please comply with the rules as laid out in the Read Before Posting thread and include any and all work you've done on these problems, even the parts you know for sure are wrong. Thank you.

Edit: Oh dear. For some reason, my message appears to have been posted three times. Sorry about that. I'll report them and hopefully a mod can delete the duplicates.