x^2+10
The values of x such as fgx= gfx is math. It comes down to finding the value of the letter X.
The graph of F(x), shown below, resembles the graph of G(x) = x2, but it has been changed somewhat. Which of the following could be the equation of F(x)?
Since g(x) is known, it helps a lot to find f(x). f(g(x)) is a new function composed by substituting x in f with g(x). For example, if g(x) = 2x + 1 and f(g(x)) = 4x2+ 4x + 1 then you you recognize that this is the square of the binomial 2x + 1, so that f(g(x)) = (f o g)(x) = h(x) = (2x + 1)2, meaning that f(x) = x2. if you have a specific example, it will be nice, because there are different ways (based on observation and intuition) to decompose a function and write it as a composite of two other functions.
-1
x2+7x=-2x2+6 3x2+7x-6=0 (3x-2)(x+3)=0 3x-2=0 or x+3=0 x=2/3 or x=-3
4
x2 + x2 = 2x2
x2 + x2 = 2x2
6x3 - x2 + 17 = 2x2 + 47 6x3 - x2 - 2x2 = 47 - 17 x2(6x - 1 - 2) = 30 this is the simplest factorisation.
x2 + 7x = 2x2 + 6 x2 - 2x2 + 7x = 6 -x2 +7x - 6 = 0 or alternatively x2 - 7x + 6 = 0
2x4
2x2 + x2 = 3x2
2x2=4 X -2=-8
The values of x such as fgx= gfx is math. It comes down to finding the value of the letter X.
The solution to the problem 2x2 is 4 (the result of multiplication).
3
2x2 = x2 - 2 Subtract x2 from both sides: x2 = -2 Take square roots: x = + or - i*sqrt(2) where i is the imaginary sqrt of -1.