college precalc

[algray09]

answer all, no, or some to make statement true:
for _____ values of x, if f(x)=x^2 and g(x)=sqrt x+2, then f(g(x)) is defined.

for _____ values of x, if f(x)=x^2+x, then f(x+h) - f(x) /h = 2x+h.

for _____ functions f, if f is invertible and decreasing, then f^-1 is increasing.

 

[Deleted member 4993]

Please show us what you have tried and exactly where you are stuck.

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Please share your work/thoughts about this problem

 

[algray09]

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING​

Please share your work/thoughts about this problem

i'm confused because in each of those, i think depends on the values used for the first one to make it defined so I think the answer is some.
then for the 2nd one i'm stuck because there is only one f value, would it be f(x^2+x+h)-f(x^2+x)/h. I also think the second one the answer is some because depends on the values used like even or odd. also depends on the values because it can't always equal 2x+h. I know that f^-1 is the inverse but confused I think its the opposite of f so increasing so I think the answer is all for that one

 

[Deleted member 4993]

answer all, no, or some to make statement true:
for _____ values of x, if f(x)=x^2 and g(x)=sqrt x+2, then f(g(x)) is defined.

for _____ values of x, if f(x)=x^2+x, then f(x+h) - f(x) /h = 2x+h.

for _____ functions f, if f is invertible and decreasing, then f^-1 is increasing.

Is it (for the first problem):

g(x)=√x + 2 ............................ this should be written as g(x)=sqrt (x)+2 ...................... or

g(x) = \(\displaystyle \sqrt{x + 2}\)............................ this should be written as g(x)=sqrt (x+2)

Similarly , fix the rest of the questions using PEMDAS and grouping symbols().

 

[Dr.Peterson]

i'm confused because in each of those, i think depends on the values used

Yes, they are asking whether it is true for some, all, or no values.

for the first one to make it defined so I think the answer is some.

Can you demonstrate this conclusion by showing a value for which it's true, and another value for which it's false?

then for the 2nd one i'm stuck because there is only one f value, would it be f(x^2+x+h)-f(x^2+x)/h. I also think the second one the answer is some because depends on the values used like even or odd. also depends on the values because it can't always equal 2x+h.

I'm assuming you meant [f(x+h) - f(x)] /h = 2x+h. Grouping symbols matter!

Check your algebra in finding f(x^2+x+h)-f(x^2+x)/h. You probably meant something like [(x^2+x+h)-(x^2+x)]/h, where you've applied the given function; it's name should go away! But it's still not quite right. If f(x) = x^2+x, what is f(x+h)? It isn't f(x)+h!

What you'll want to do is to fully simplify the expression to make it look as much like 2x+h as you can, so you can make a firm conclusion (either by examples as in the first, or by some convincing reasoning).

I know that f^-1 is the inverse but confused I think its the opposite of f so increasing so I think the answer is all for that one

"Opposite" is not clearly defined, but you may be thinking correctly. Can you sketch such a function and it's inverse, and explain why that would always be true?