Question

if f(x)= a^x then show that f(m)^n= f(mn) and f(m-n)= f(m)/f(n)​

Answer 1

Step-by-step explanation:

f(x)= a^x ----eqn1

replace x by m in eqn1

f(m) =a^m

f(m) ^n=a^m^n=a^mn(formula power to power can be mulplied)

replace x by mn in eqn1

f(mn) =a^mn

so f(m) ^n =f(mn)

hence proved

replace x by m-n in eqn1.

f(m-n) =a^(m-n)

replace x by m

f(m) =a^m

replace x by n

f(n) =a^n

f(m) /f(n) =a^m/a^n=a^(m-n)(formula division of same a power different is a to power of difference of power)

f(m-n)= f(m)/f(n)

hence proved