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3 years ago

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If f(z)=m^z - n^z, and f(1)=2, f(2)=8. Find f(3).

1 answer:

Marina CMI [18]3 years ago

3 0

If f(z)=m^z - n^z <span>and f(1)=2, f(2)=8
then
m - n = 2 so m = n + 2
m^2 - n^2 = 8

substitute </span>m = n + 2 into m^2 - n^2 = 8

so
m^2 - n^2 = 8
(n + 2)^2 - n^2 = 8
n^2 + 4n + 4 - n^2 = 8
4n = 4
n = 1

m = n + 2 = 1 + 2 = 3

so f(z) = 3^z - 1^z

if z = 1 the f(1) = 3^1 - 1^1 = 2
if z = 2 the f(2) = 3^2 - 1^2 = 9 - 1 = 8
if z = 3 the f(3) = 3^3 - 1^2 = 27 - 1 = 26

answer
f(3) = 26

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