If the expression f2+g4−2f+1 is rewritten in the form a2+(g2)2, what must be the value of a?

Answer 1

f^2 + g^4 -2f + 1

= (g^2)^2 + a^2

= g^4 +a^2

a^2 = f^2 +g^4 -2f +1 -g^4

a^2 = f^2 -2f + 1

a^2 = (f-1)^2

a = + or - (f-1)

a = f-1 or 1-f

but a or the 1st letters of the alphabet tend to be used as constants, real numbers, not variables or functions.

the math notation on the problem is a little unclear. f and g are used to indicate functions

f2 or g4 seem to mean f^2 and g^4, but it's not certain.

still when the answer simplies so much to f-1 or 1-f, that's probably the answer you want

a= f-1, or 1-f