Solve Composite Function: g(f(x)) = 225?

Click For Summary

Homework Help Overview

The discussion revolves around evaluating the composite function g(f(x)), where f(x) is defined as a polynomial function and g(x) is a constant function. Participants are exploring the implications of substituting one function into another.

Discussion Character

  • Exploratory, Conceptual clarification

Approaches and Questions Raised

  • Some participants attempt to evaluate g(f(x)) by substituting values into the functions, while others question the nature of g(x) as a constant function. There is also a discussion about the correct interpretation of plugging a function into another function.

Discussion Status

The conversation includes attempts to clarify the evaluation of composite functions and the nature of constant functions. Some guidance is offered regarding understanding the relationship between g and f, but no consensus is reached on the evaluation process.

Contextual Notes

Participants express uncertainty about the definitions and operations involving composite functions, particularly in the context of constant functions and polynomial expressions.

Loppyfoot
Messages
192
Reaction score
0

Homework Statement


If f(x) = x3+3x2+4x+5 and g(x)=5, then g(f(x)) = ?


Homework Equations





The Attempt at a Solution


I don't know if I am correct.
g(f(x)) =
g(x3+3x2+4x+5)= 225?

I plugged 5 into the equation. Am I right?
 
Physics news on Phys.org
Loppyfoot said:

Homework Statement


If f(x) = x3+3x2+4x+5 and g(x)=5, then g(f(x)) = ?


Homework Equations





The Attempt at a Solution


I don't know if I am correct.
g(f(x)) =
g(x3+3x2+4x+5)= 225?

I plugged 5 into the equation. Am I right?

If you plugged 5 into f(x), then you calculated f(5) = f(g(x)), since g(x) = 5. You want to find g(f(x)), which means plug f(x) into g(x).

If you're having trouble, maybe ask yourself, what's g(1), g(10), g(1000)? Once you see a pattern, then g(f(x)) shouldn't be much harder.
 
How do I plug a function into an integer? Would g(f(x)) just be 5?
 
g(x) isn't an integer. It's called a constant function. And yep, g(f(x))=5.
 

Similar threads

Finding the domain of a composite function
  • · Replies 10 ·
Replies
10
Views
2K
Curiosity about why this is not a Function composition
  • · Replies 7 ·
Replies
7
Views
4K
How does this composite function simplify to 2(2^x) ?
  • · Replies 3 ·
Replies
3
Views
2K
Domain of a composite function
  • · Replies 4 ·
Replies
4
Views
2K
Spivak chapter 3 problem 24 - proof of a composition
  • · Replies 2 ·
Replies
2
Views
2K
Solution of inequality of composite function involving inverse
  • · Replies 13 ·
Replies
13
Views
2K
How to identify the type of function?
  • · Replies 23 ·
Replies
23
Views
4K
Is f Injective? Understanding the Composition of Functions
  • · Replies 3 ·
Replies
3
Views
2K
Composite and Inverse Functions Problem
  • · Replies 3 ·
Replies
3
Views
2K
Counter example to: if f*g is inv then f & g are inv
  • · Replies 2 ·
Replies
2
Views
2K