What are the solutions to the equation f=f^2 ?

The solutions to the equation f=f^2 are f=1,f=0

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f=f^2

f = f^{2}

f = 1, f = 0

Solution steps

f = f^{2}

Switch sides

f^{2} = f

Move

f

to the left side

f^{2} - f = 0

Solve with the quadratic formula

f_{1, 2} = \frac{- ( - 1 ) \pm ( - 1 ) ^{2} - 4 \cdot 1 \cdot 0}{2 \cdot 1}

(- 1)^{2} - 4 \cdot 1 \cdot 0 = 1

f_{1, 2} = \frac{- ( - 1 ) \pm 1}{2 \cdot 1}

Separate the solutions

f_{1} = \frac{- ( - 1 ) + 1}{2 \cdot 1}, f_{2} = \frac{- ( - 1 ) - 1}{2 \cdot 1}

f = \frac{- ( - 1 ) + 1}{2 \cdot 1} : 1

f = \frac{- ( - 1 ) - 1}{2 \cdot 1} : 0

The solutions to the quadratic equation are:

f = 1, f = 0

y = (x + 5)^{2} - 1

f (x) = x^{3} + 3 x^{2} - 4 x

f (s) = s + 2

f (x) = 2 cos (x) + cos^{2} (x)

What are the solutions to the equation f=f^2 ?
The solutions to the equation f=f^2 are f=1,f=0
Find the zeros of f=f^2
The zeros of f=f^2 are f=1,f=0