If f(x)=x2+10, find and simplify the following:
(a) f(t+8)=
(b) f(t5+8)=
(c) f(5)=
(d) 5f(t)=
(e) (f(t))2+8=
Actually, it's not homework. It's a practice problem that I don't even get credit for. I've done the problem multiple times but didn't think I should type up all my work for the wrong answers that I keep getting. I don't know who the other person is that is posting but mine is a real question and it's wrong for you to question my intentions because you don't know me as a student. If I needed help with actual homework I would go to my teacher but this is a practice problem that I was working on so I just thought I would post it for help. That's the point of the website, to HELP students with their homework and that's what I wanted. If you don't have anything nice to say, don't say it at all because all I am is a student looking for some help on ONE problem.
To solve these problems, we will substitute expressions into the function f(x) and simplify the resulting expressions. Let's start with the given function f(x) = x^2 + 10.
(a) To find f(t + 8), we need to replace x in the original function f(x) with t + 8.
Substituting x = t + 8 in f(x), we get:
f(t + 8) = (t + 8)^2 + 10
To simplify, we expand the squared term:
f(t + 8) = (t + 8)(t + 8) + 10
= t^2 + 16t + 64 + 10
Simplifying further, we combine like terms:
f(t + 8) = t^2 + 16t + 74
(b) To find f(t5 + 8), we substitute x = t5 + 8 into the function f(x):
f(t5 + 8) = (t5 + 8)^2 + 10
Expanding the squared term, we get:
f(t5 + 8) = (t^2)(5)^2 + 2(t)(5)(8) + 8^2 + 10
= t^2(25) + 10t + 64 + 10
Again, we combine like terms:
f(t5 + 8) = 25t^2 + 10t + 74
(c) To find f(5), we substitute x = 5 into the function f(x):
f(5) = (5)^2 + 10
= 25 + 10
= 35
Therefore, f(5) simplifies to 35.
(d) To find 5f(t), we multiply the given function f(x) by 5:
5f(t) = 5*(t^2 + 10)
= 5t^2 + 50
So, 5f(t) simplifies to 5t^2 + 50.
(e) To find (f(t))^2 + 8, we need to evaluate f(t) and then square the result:
(f(t))^2 + 8 = (t^2 + 10)^2 + 8
Expanding the squared term, we get:
(f(t))^2 + 8 = (t^2 + 10)(t^2 + 10) + 8
= t^4 + 10t^2 + 10t^2 + 100 + 8
Combining like terms, we simplify further:
(f(t))^2 + 8 = t^4 + 20t^2 + 108
Therefore, (f(t))^2 + 8 simplifies to t^4 + 20t^2 + 108.
More homework-dumping by someone with a strange identity crisis.
You can get help if you post what YOU THINK for each of your problems. No one here will do your work for you.
And just stick to one name. We know you're the same person posting from the same computer!!