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Let $f,gcolonmathbb Rtomathbb R$, where $g(x)=1-x+x^2$ and $f(x) = ax+b$. If $(gcirc f)(x) = 9x^2-9x+3$, determine $a$, $b$. [duplicate]

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1

$begingroup$

This question already has an answer here:

• 
  Using function compositions to determine variable values
  
  1 answer
  
  

I’m struggling with the following problem in my textbook

Let $f,gcolonmathbb Rtomathbb R$, where $g(x)=1-x+x^2$ and $f(x) = ax+b$. If $(gcirc f)(x) = 9x^2-9x+3$, determine $a$, $b$.

What I’ve tried:

So I know $(gcirc f)(x) = g(f(x))$ and if I substitute the functions I get $1-(ax+b)+(ax+b)^2$ and I also know that that equals to $9x^2-9x+3$.

Now this is where I get stuck

I’m not sure how to isolate a and b to find there values,I’ve tried rearranging $1-(ax+b)+(ax+b)^2 = 9x^2-9x+3$ into multiple different expressions to get something that I might be able to solve but after a few hours I didn’t get anywhere.

functions discrete-mathematics

share|cite|improve this question

edited Mar 13 at 18:54

Ennar

14.8k32445

asked Mar 13 at 18:48

NicolasomeNicolasome

276

$endgroup$

marked as duplicate by Lord Shark the Unknown, Community♦ Mar 14 at 4:23

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I like that you’ve thought about this question and provided some evidence that you worked on it, at least a little bit. I’d recommend taking a look at some of the MathJax tutorials on this site so your posts are more readable (it isn’t too hard, but it might feel clunky at first; the payoff is that your posts will be more likely to receive positive attention). +$1$.
  $endgroup$
  – Clayton
  Mar 13 at 18:55
  
  

  
  
  
  

add a comment | 

1

$begingroup$

This question already has an answer here:

• 
  Using function compositions to determine variable values
  
  1 answer
  
  

I’m struggling with the following problem in my textbook

Let $f,gcolonmathbb Rtomathbb R$, where $g(x)=1-x+x^2$ and $f(x) = ax+b$. If $(gcirc f)(x) = 9x^2-9x+3$, determine $a$, $b$.

What I’ve tried:

So I know $(gcirc f)(x) = g(f(x))$ and if I substitute the functions I get $1-(ax+b)+(ax+b)^2$ and I also know that that equals to $9x^2-9x+3$.

Now this is where I get stuck

I’m not sure how to isolate a and b to find there values,I’ve tried rearranging $1-(ax+b)+(ax+b)^2 = 9x^2-9x+3$ into multiple different expressions to get something that I might be able to solve but after a few hours I didn’t get anywhere.

functions discrete-mathematics

share|cite|improve this question

edited Mar 13 at 18:54

Ennar

14.8k32445

asked Mar 13 at 18:48

NicolasomeNicolasome

276

$endgroup$

marked as duplicate by Lord Shark the Unknown, Community♦ Mar 14 at 4:23

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

• 
  
  
  

  
  1
  

  
  
  
  
  
  

  
  $begingroup$
  I like that you’ve thought about this question and provided some evidence that you worked on it, at least a little bit. I’d recommend taking a look at some of the MathJax tutorials on this site so your posts are more readable (it isn’t too hard, but it might feel clunky at first; the payoff is that your posts will be more likely to receive positive attention). +$1$.
  $endgroup$
  – Clayton
  Mar 13 at 18:55
  
  

  
  
  
  

add a comment | 

$begingroup$

This question already has an answer here:

• 
  Using function compositions to determine variable values
  
  1 answer
  
  

I’m struggling with the following problem in my textbook

Let $f,gcolonmathbb Rtomathbb R$, where $g(x)=1-x+x^2$ and $f(x) = ax+b$. If $(gcirc f)(x) = 9x^2-9x+3$, determine $a$, $b$.

What I’ve tried:

So I know $(gcirc f)(x) = g(f(x))$ and if I substitute the functions I get $1-(ax+b)+(ax+b)^2$ and I also know that that equals to $9x^2-9x+3$.

Now this is where I get stuck

I’m not sure how to isolate a and b to find there values,I’ve tried rearranging $1-(ax+b)+(ax+b)^2 = 9x^2-9x+3$ into multiple different expressions to get something that I might be able to solve but after a few hours I didn’t get anywhere.

functions discrete-mathematics

share|cite|improve this question

edited Mar 13 at 18:54

Ennar

14.8k32445

asked Mar 13 at 18:48

NicolasomeNicolasome

276

$endgroup$

share|cite|improve this question

edited Mar 13 at 18:54

Ennar

14.8k32445

asked Mar 13 at 18:48

NicolasomeNicolasome

276

share|cite|improve this question

edited Mar 13 at 18:54

Ennar

14.8k32445

asked Mar 13 at 18:48

NicolasomeNicolasome

276

edited Mar 13 at 18:54

Ennar

14.8k32445

edited Mar 13 at 18:54

Ennar

14.8k32445

asked Mar 13 at 18:48

NicolasomeNicolasome

276

asked Mar 13 at 18:48

NicolasomeNicolasome

276

2 Answers
2

active

oldest

votes

3

$begingroup$

Replace $x$ with $0$ then $1-(a cdot 0+b)+(a cdot 0+b)^2=9(0)^2-9(0)+3$

Upon simplifying both sides you get $1-b+b^2=3 $ Solve for b

Find $a$ in a similar way with using the $b$ you found. Choose a different $x$ though.

share|cite|improve this answer

answered Mar 13 at 18:50

randomgirlrandomgirl

2,9791915

$endgroup$

add a comment | 

2

$begingroup$

Hint: Expand $(ax+b)^2 - (ax+b) + 1$ and then match the coefficients according to $x^2$ and $x$ with the function $9x^2 - 9x + 3$.

share|cite|improve this answer

answered Mar 13 at 18:59

bjcolby15bjcolby15

1,50011016

$endgroup$

add a comment | 

3

$begingroup$

Replace $x$ with $0$ then $1-(a cdot 0+b)+(a cdot 0+b)^2=9(0)^2-9(0)+3$

Upon simplifying both sides you get $1-b+b^2=3 $ Solve for b

Find $a$ in a similar way with using the $b$ you found. Choose a different $x$ though.

share|cite|improve this answer

answered Mar 13 at 18:50

randomgirlrandomgirl

2,9791915

$endgroup$

add a comment | 

3

$begingroup$

Replace $x$ with $0$ then $1-(a cdot 0+b)+(a cdot 0+b)^2=9(0)^2-9(0)+3$

Upon simplifying both sides you get $1-b+b^2=3 $ Solve for b

Find $a$ in a similar way with using the $b$ you found. Choose a different $x$ though.

share|cite|improve this answer

answered Mar 13 at 18:50

randomgirlrandomgirl

2,9791915

$endgroup$

add a comment | 

$begingroup$

Replace $x$ with $0$ then $1-(a cdot 0+b)+(a cdot 0+b)^2=9(0)^2-9(0)+3$

Upon simplifying both sides you get $1-b+b^2=3 $ Solve for b

Find $a$ in a similar way with using the $b$ you found. Choose a different $x$ though.

share|cite|improve this answer

answered Mar 13 at 18:50

randomgirlrandomgirl

2,9791915

$endgroup$

share|cite|improve this answer

answered Mar 13 at 18:50

randomgirlrandomgirl

2,9791915

answered Mar 13 at 18:50

randomgirlrandomgirl

2,9791915

answered Mar 13 at 18:50

randomgirlrandomgirl

2,9791915

2

$begingroup$

Hint: Expand $(ax+b)^2 - (ax+b) + 1$ and then match the coefficients according to $x^2$ and $x$ with the function $9x^2 - 9x + 3$.

share|cite|improve this answer

answered Mar 13 at 18:59

bjcolby15bjcolby15

1,50011016

$endgroup$

add a comment | 

2

$begingroup$

Hint: Expand $(ax+b)^2 - (ax+b) + 1$ and then match the coefficients according to $x^2$ and $x$ with the function $9x^2 - 9x + 3$.

share|cite|improve this answer

answered Mar 13 at 18:59

bjcolby15bjcolby15

1,50011016

$endgroup$

add a comment | 

$begingroup$

Hint: Expand $(ax+b)^2 - (ax+b) + 1$ and then match the coefficients according to $x^2$ and $x$ with the function $9x^2 - 9x + 3$.

share|cite|improve this answer

answered Mar 13 at 18:59

bjcolby15bjcolby15

1,50011016

$endgroup$

share|cite|improve this answer

answered Mar 13 at 18:59

bjcolby15bjcolby15

1,50011016

answered Mar 13 at 18:59

bjcolby15bjcolby15

1,50011016

answered Mar 13 at 18:59

bjcolby15bjcolby15

1,50011016