Thread: Algebra Proofs

(1) If f(x) = a^x, show that f(A + B) = f(A) * f(B)

(2) If f(x) = a^x, show that f(Ax) = [f(x)]^A

Originally Posted by magentarita

(1) If f(x) = a^x, show that f(A + B) = f(A) * f(B)

(2) If f(x) = a^x, show that f(Ax) = [f(x)]^A

f(x) = a^x
f(A + B)=a^(A + B)
=a^A*a^B
but a^A =f(A) and a^B=f(B)
putting these values we get
f(A + B) = f(A) * f(B) hence proved
2)f(x) = a^x
f(Ax) =a^(Ax)
=(a^x)^A
=[f(x)]^A
therfor
f(Ax) =[f(x)]^A hence proved

(1)




(2)

Wonderfully done!