Exercise 4.2 Show that: a) FPC Vx(Fx -> (FxVGx)) b) FPC Vx(FxAGx)→ (\xFx ^\xGx) c) FPC VxFx→\yFy d) Vx(Fx→Gx), Vx(Gx→Hx) FPC\x(Fx→Hx) e) xFx, Vx(Fx→Gx) Fpc 3xGx f) FPC 3xVyRxy->\yxRxy g) FPC (VxVy(RxyRyx)^ Rab)→ z Rza РС
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- Determine whether each of these functions is a bijection from R to R. f(x) = x^2 + 1 f(x) =(x^2 +1)/(x^2 + 2) f(x) =IxI f(x) =x/2Differentiate the following function. y=x(x³ +5) ³ Choose the correct setup below to differentiate the function. [x(x5 +5)³] = (x)•. J :(x5 + 5)³) + ((x³ +5)³).) dx d « (x5 + 5)³] = « - -(x* + 5) ³) - ((x³ +5)³).) dx dx [x (x* +5)³]=2• [x(x° +5) ³].[x (x* + 5) ³] dx dx d d Ix(x5 +5)³]= x) • 3 (a5 +5) + ((x³ +5) ³) · x) d [x (x5 + 5)³] = (x) • ) + ( (x5 + 5) ³) • -c() + ( (x5 +5) ³) • (x5 + 5) ³) dx dx dx d [x(x* + 5)³ : dx