MHB What is the Result of Plugging g(x) Into f(x)?

mathdad
Messages
1,280
Reaction score
0
The question wants (f•g)(x). I understand this to be
f(g(x)).

This means to plug the value of g(x) into every x I see in f(x) and simplify.

f(3x^2) = 4(3x^2) + 7

f(3x^2) = 12x^2 + 7

So, f(g(x)) = 12x^2 + 7.

This is not the book's answer.
 
Mathematics news on Phys.org
RTCNTC said:
The question wants (f•g)(x). I understand this to be
f(g(x)).

This means to plug the value of g(x) into every x I see in f(x) and simplify.

f(3x^2) = 4(3x^2) + 7

f(3x^2) = 12x^2 + 7

So, f(g(x)) = 12x^2 + 7.

This is not the book's answer.
What are your functions f(x), g(x)? Can't help you if we don't know that! Please give us the whole problem.

-Dan
 
f(x) = 4x + 7

g(x) = 3x^2
 
f(x) = 4x + 7

g(x) = 3x^2

So, f(g(x)) = 12x^2 + 7.

This is not the book's answer.

For the two functions you cite, your solution is correct ... what is the "book answer" ?
 
Book's answer:

12x^2+21x.
 

Thread 'What Exactly is Dirac’s Delta Function? - Insight'

Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...
View full post »

Thread 'Fermat's Last Theorem'

Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
View full post »

Thread 'Useless continued fraction for 1'

I'm interested to know whether the equation $$1 = 2 - \frac{1}{2 - \frac{1}{2 - \cdots}}$$ is true or not. It can be shown easily that if the continued fraction converges, it cannot converge to anything else than 1. It seems that if the continued fraction converges, the convergence is very slow. The apparent slowness of the convergence makes it difficult to estimate the presence of true convergence numerically. At the moment I don't know whether this converges or not.
View full post »

Similar threads

MHB Proving Equivalence of f(x) and g(x)
Replies
2
Views
1K
A Why the triangle inequality is greater than the 2 max{f(x),g(x)}
Replies
1
Views
1K
MHB Fixed point,, Jacobi- & Newton Method, Linear Systems
Replies
7
Views
2K
MHB How to Solve a Composition of Functions g(f(x))?
Replies
9
Views
2K
MHB Solving 8 Roots: Can 3 Quadratic Polynomials Fulfill $f(g(h(x)))=0$?
Replies
1
Views
1K
MHB Inequality solve (x+1)/6<x-(3x-2)/4
Replies
2
Views
1K
MHB If f(3x) = f(3) + f(x) , then prove that : f(1) = f(3) =f(9) = f(27) = f(81) = 0
Replies
6
Views
2K
I My attempt to understand horizontal transformations of functions
Replies
6
Views
1K
MHB Solving g(x)-h(x) <0: Find a, b, c, d
Replies
2
Views
1K
MHB F(x) = x2-7 and g(x) = x- 3, find (f º g )(x) [2]
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top