MathLabs

Problem 5

Find all functions f:R→Rf:\mathbb R\to\mathbb R such that (f(x)+f(z))(f(y)+f(t))=f(xy−zt)+f(xt+yz)(f(x)+f(z))(f(y)+f(t))=f(xy-zt)+f(xt+yz) for all real numbers x,y,z,tx,y,z,t.
Step 1 of 3: Handle constants
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In plain words

Handle constants

4c2=2c4c^2=2c
Detailed analysis

For f≡cf\equiv c, the equation gives 4c2=2c4c^2=2c, so c=0c=0 or c=1/2c=1/2, and both work.