If f(x) = 2x + 1 and g(x) = x2, find the values of x for which gf(x) = fg(x).

x = 0, x = - 2

Step-by-step explanation:

Find g(f(x)) and f(g(x))

g(f(x)) = g(2x + 1) = (2x + 1)²

f(g(x)) = f(x²) = 2x² + 1

Thus

(2x + 1)² = 2x² + 1 ← expand left side using FOIL

4x² + 4x + 1 = 2x² + 1 ← subtract 2x² + 1 from both sides

2x² + 4x = 0 ← in standard form

2x(x + 2) = 0 ← in factored form

Equate each factor to zero and solve for x

2x = 0 ⇒ x = 0

x + 2 = 0 ⇒ x = - 2

WRONG ANSWER

I did not read fg(x) and gf(x) but only g(x) and f(x)

x₁= 1-√2  and x₂=1+√2

Step-by-step explanation:

you need to find where the system of the two given equation has solutions

one equation is linear, the other one is a parabolic equation, there will be at most 2 points where they cross path (but there could be even 1 point or even none)

you need to find where 2x+1 = x^2  or  x^2-2x -1 = 0

using the quadratic formula x=(−b±√b2−4ac)/2a

a=1 b=-2 c=-1

you will get two solutions x₁= 1-√2  and x₂=1+√2

i think that you should ask google for the answer to that problem because if we don't know it google does

make sure you have version 2.50

try looking in the very back of the book : )

step-by-step explanation:

you can download it here