Question

Please help! For all values of x, F(x)= x-1 And G(x)=2x^2+3 Solve fg(x)= gf(x)

Answer 1

Answer:

$\boxed{\sf \ \ \ x=\dfrac{3}{4} \ \ \ }$

Step-by-step explanation:

hello,

f(x)=x-1

$g(x)=2x^2+3$

so

$fog(x)=f(g(x))=f(2x^2+3)=2x^2+3-1=2x^2+2 \ and \\gof(x)=g(f(x))=g(x-1)=2(x-1)^2+3=2x^2-4x+2+3=2x^2-4x+5 \ \ So\\\fog(x)=gof(x) <=>2x^2+2=2x^2-4x+5\\<=>4x=5-2=3\\<=>x=\dfrac{3}{4}$

hope this helps

Answer 2

$\frac{3}{4}$

The composition of a function is a process in which two functions $f,g$, are combined to produce a new function, $h$, with the formula $h(x)=g(f(x))$. It means that the $g$ function is being applied to the $x$ function.

$f(x)=x-1\\g(x)=2x^2+3$

$f(g(x))=f(2x^2+3)$

            $=2x^2+3-1\\=2x^2+2$

$g(f(x))=g(x-1)$

           $=2(x-1)^2+3\\=2x^2+2-4x+3\\=2x^2-4x+5$

$f(g(x))=g(f(x))$

$2x^2+2=2x^2-4x+5$

       $4x=3$

        $x=\frac{3}{4}$

For more information:

https://brainly.com/question/12431044?referrer=searchResults