What is the answer to f(x)=f(x)(x)^{-1}(x) ?

The answer to f(x)=f(x)(x)^{-1}(x) is x\ne 0

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f(x)=f(x)(x)^{-1}(x)

f (x) = f (x) (x)^{- 1} (x)

x \neq = 0

Solution steps

f (x) = f (x) x^{- 1} (x)

Refine

f (x) = f (x)

Subtract

f (x)

from both sides

f (x) - f (x) = f (x) - f (x)

Simplify

0 = 0

Both sides are equal

True for all x

Verify Solutions

Find undefined (singularity) points:

x = 0

Since the equation is undefined for:

0

x \neq = 0

y^{2} = 4 (x + 2 y)

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

x^{2} + 6 x - m (x) = 0

- x^{2} + 4 x + 4 y = 0

x^{2} - 6 x - 4 y = - 1

What is the answer to f(x)=f(x)(x)^{-1}(x) ?
The answer to f(x)=f(x)(x)^{-1}(x) is x\ne 0