Find functions ... where [variables] are real constants.

[student882]

I've searched but can't seem to find what this means:
Consider f(x)=x³+5 and g(x)=x+3/x². Find functions f(ax+b) and g(x+h), where a, b, h are real constants.

Note: This is a question for a school assignment - please don't give me the answer.

...just don't know what they want me to do. I am new to this (still catching up) so if it's possible to simplify the merged function, perhaps a hint or two?



(Thanks in advance to anyone who comments!)

 

[stapel]

I've searched but can't seem to find what this means:
Consider f(x)=x³+5 and g(x)=x+3/x². Find functions f(ax+b) and g(x+h), where a, b, h are real constants.

I think, by "find", they just mean "write out and simplify". So, for instance, if they'd said "Find f(b + cx)", they'd have been looking for the simplification of f(b + cx) = (b + cx)^3 + 5. But, to be certain, check in the section of the book that generated this exercise; there's likely a similar example worked out in the text.

 

[fcabanski]

The first answer has it right. The exercise is to prepare you for using the definition of derivative.

f(x+3a) for f(x) = x^3 + x is (x+3a)^3 + x+3a.

 

[student882]

Okay, but then am I supposed to substitute 'real constants' in at random?


I've handed the assignment in, so anything else said is mainly for the sake of others...
(Unfortunately don't have the textbook yet Stapel, but a valid point, thanks for the replies!)

 

[fcabanski]

No, it's not at random. The real constants go into the places of a, b and h.

For example:

f(x)=x³+5. Find function f(ax+b), where a=3 and b=2.

f(ax+b) = (3x+2)^3 + 5

 

[Quaid]

am I supposed to substitute 'real constants' in at random?

No. The answer for f(ax+b) will contain the symbols x, a, & b, and the answer for g(x+h) will contain the symbols x & h.

If they wanted you to substitute Real values for any symbols, they would need to use the specific instruction "substitute".

When they say, "where a, b, h are real constants", it's just to let you know that none of the symbols a, b, and h represent variables; they each stand for some fixed quantity which is not important for this exercise.



PS: You typed x+3/x^2

If the numerator is x+3, then you need to type grouping symbols around it.

(x+3)/x^2