f(x)=x-1 g(x)=x^2 solve the equation gf(x)=f^-1 (x)

title says it all

thanks in advance

f(x)=x-1 g(x)=x^2

solve the equation gf(x)=f^-1(x)

I assume by f^-1 (x) you mean the inverse function of f(x) ? If so I think the following is right...

g(f(x)) = g(x-1)
= (x-1)^2

lets say f(x) = y , so y = x-1.
to get the inverse, switch y and x: x =y-1
y = x+1
= f^-1 (x)

g(f(x)) = f^-1 (x)
(x-1)^2 = x + 1
x^2 -2x +1 = x +1
x^2 - 3x = 0
x(x-3) = 0

so x = 0 or x = 3

i hope that helps, do you have the answers? let me know if it is correct

that's what i keep getting but my workbook says x^2-1 (without working out a final value of x) and then im like, wat?

so it doesnt give you a value of x as the answer even though thats what the question asked? does it just give the answer or any working out?

just the answer

the book dosent want a value of x just a simplified final equation ... i fink

... ...

that's what i keep getting but my workbook says x^2-1 (without working out a final value of x) and then im like, wat?