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

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

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

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

x \neq = 0

Solution steps

f (x) x^{- 1} (x) = f (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} - 6 y + 16 x + 41 = 0

y^{2} + 50 x = - 1

x^{2} - 6 x - 8 y + 17 = 0

0 = 10 x - 1 - 6 y - x^{2}

5 y^{2} + 50 x = 0

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