MHB F(x) = x2-7 and g(x) = x- 3, find (f º g )(x) [2]

  • Thread starter Thread starter trevor
  • Start date Start date
AI Thread Summary
To find (f º g)(x), substitute g(x) into f(x), resulting in (x - 3)² - 7. For (g º f)(x), substitute f(x) into g(x), yielding x² - 7 - 3. The discussion also touches on finding the inverse functions f⁻¹(x) and g⁻¹(x), but the focus remains on the composition of the functions. The user expresses confusion about the notation and seeks clarification on how to proceed with the calculations. Understanding function composition is crucial for solving these problems effectively.
trevor
Messages
6
Reaction score
0
Let f(x) = x2-7 and g(x) = x- 3
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f-1 (x) = g-1(x)
 
Mathematics news on Phys.org
trevor said:
Let f(x) = x2-7 and g(x) = x- 3
Find:
i. (f º g )(x) [2]
ii. (g º f) (x) [2]
iii. f-1 (x) = g-1(x)

Hi trevor. What have you tried so far? :)
 
Joppy said:
Hi trevor. What have you tried so far? :)

I am clueless
 
(f o g)(x) means f(g(x)). That means, you replace the value in f(x) with g(x), thus your x2 - 7 will become (g(x))2 - 7. Can you continue from here?
 

Thread 'Non-orthogonal bases'

Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
View full post »

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 »

Similar threads

I Is g(x) Equal to g(a) If Their Integrals Are Equivalent?
Replies
20
Views
2K
A Why the triangle inequality is greater than the 2 max{f(x),g(x)}
Replies
1
Views
1K
I Why fixed point iteration of ##x^3 = 1-x^2## doesn't converge when ##x_0= 0##
Replies
16
Views
508
MHB Solving 8 Roots: Can 3 Quadratic Polynomials Fulfill $f(g(h(x)))=0$?
Replies
1
Views
1K
MHB [ASK] Seemingly Simple Limit Question but I have no Idea
Replies
2
Views
1K
MHB How to Solve a Composition of Functions g(f(x))?
Replies
9
Views
2K
MHB Solving g(x)-h(x) <0: Find a, b, c, d
Replies
2
Views
1K
MHB Proving Equivalence of f(x) and g(x)
Replies
5
Views
1K
MHB Max Value of $b$ for Real Roots of $f(x)$ and $g(x)$
Replies
2
Views
1K
B Proof of Chain Rule: Understanding the Limits
Replies
3
Views
1K

Hot Threads

Recent Insights

Back
Top