Question

f(x)=ax+b and g(x)=1-x+x^2 and if gof=9x^2+9x+3 determine a and b

Answer 1

yeah....it helps you to know

Answer 2

Answer:

If $f(x)=ax+b$ , $g(x)=1-x+x^2$, and  $gof=9x^2+9x+3$ then $a=3$ and $b=2$.

Step-by-step explanation:

We have two functions as

$f(x)=ax+b$ and

$g(x)=1-x+x^2$

and their composite function is given as

$gof=9x^2+9x+3$

Now we have to calculate the value of $"a"and "b"$

Step 1 of 2

First, we will calculate the value of $gof$ as

$gof=g{f(x)}\\ =g(ax+b)\\=1-(ax+b)+(ax+b)^2\\=1-ax-b+a^2x^2+b^2+2abx\\=a^2x^2+(2ab-a)x+(1+b^2-b)$       .....(1)

Step 2 of 2

Now comparing the above value $a^2x^2+(2ab-a)x+(1+b^2-b)$ with the given value $9x^2+9x+3$ we get

$a^2=9$ and $2ab-a=9$

⇒$a=3$

then $2.3b-3=9$

⇒$b=2$

Hence the value of a and b are 3 and 2 respectively.