If (f o g)= 16x + 7 and g(x)= 2x - 1 , find f(x)

  • Thread starter Thread starter Andolph23
  • Start date Start date
AI Thread Summary
To find f(x) given (f o g) = 16x + 7 and g(x) = 2x - 1, substitute g(x) into the composite function. The correct approach involves assuming f(x) is a linear function of the form Ax + B. By substituting g(x) into f(g(x)), the goal is to equate it to 16x + 7 to solve for A and B. The discussion also suggests verifying the result by checking if f(g(x)) returns the original expression. The conversation highlights the importance of methodical substitution in function composition.
Andolph23
Messages
4
Reaction score
0

Homework Statement



If (f o g)= 16x + 7 and g(x)= 2x - 1 , find f(x)


The Attempt at a Solution



I haven't done a problem like this in awhile so I don't remember exactly what to do. I think you plug g(x) into (f o g) to get 32x - 9 but I'm not sure if that's correct.

Homework Statement

 
Physics news on Phys.org
Andolph23 said:

Homework Statement



If (f o g)= 16x + 7 and g(x)= 2x - 1 , find f(x)


The Attempt at a Solution



I haven't done a problem like this in awhile so I don't remember exactly what to do. I think you plug g(x) into (f o g) to get 32x - 9 but I'm not sure if that's correct.

Homework Statement


If this is correct, you should try f(g(x)) and see if you get what it was originally

P.S. Notice your trying to get f(x)
 
Suppose that f(x) = Ax + B, a linear function. Given that, and that g(x) = 2x - 1, what is (f o g)(x)?
(Ignore for a moment that (f o g)(x) was already given.)

P.S. This should really be in the Precalculus subforum.
 
What is (f○g○g-1)(x) ?
 
SammyS said:
What is (f○g○g-1)(x) ?

Wow, your good:wink: Didn't even think of that.
 

Thread 'Finding the number of ways to arrange identical balls in a circle (3 different colors)'

I tried to combine those 2 formulas but it didn't work. I tried using another case where there are 2 red balls and 2 blue balls only so when combining the formula I got ##\frac{(4-1)!}{2!2!}=\frac{3}{2}## which does not make sense. Is there any formula to calculate cyclic permutation of identical objects or I have to do it by listing all the possibilities? Thanks
View full post »

Thread 'Greatest possible value of a constant in polynomial'

Since ##px^9+q## is the factor, then ##x^9=\frac{-q}{p}## will be one of the roots. Let ##f(x)=27x^{18}+bx^9+70##, then: $$27\left(\frac{-q}{p}\right)^2+b\left(\frac{-q}{p}\right)+70=0$$ $$b=27 \frac{q}{p}+70 \frac{p}{q}$$ $$b=\frac{27q^2+70p^2}{pq}$$ From this expression, it looks like there is no greatest value of ##b## because increasing the value of ##p## and ##q## will also increase the value of ##b##. How to find the greatest value of ##b##? Thanks
View full post »

Similar threads

Find the range of the function ##f(x) = \frac{e^{2x}-e^x+1} {e^{2x}+e^x+1}##
Replies
8
Views
3K
Understanding the graphical effect of f(x+a)
Replies
19
Views
2K
How to Do (f o g)(1) Function Problem?
Replies
3
Views
26K
Composite Functions, please confirm
Replies
13
Views
2K
Comparing Lag Between f(x,t) and g(x,t): Homework Equations and Solutions"
Replies
1
Views
1K
Counter example to: if f*g is inv then f & g are inv
Replies
2
Views
2K
Comparing f(x) and g(x) for All x in R
Replies
3
Views
2K
Range of f(x): Intersection of h(x) and g(x) Ranges
Replies
13
Views
3K
Solve ##\dfrac{3x-6}{5-x}+\dfrac{11-2x}{10-4x}=3\dfrac{1}{2}##
Replies
3
Views
2K
Compute f°g & g°f: Domain & Codomain Explained
Replies
7
Views
2K

Hot Threads

Recent Insights

Back
Top