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