Question

$f(x) = {2}^{3x - 2}$
Find
i)
${f}^{ - 1} (2)$
ii)
${f}^{2} (x)$
​

Answer 1

Step-by-step explanation:

We have,

$f(x) = {2}^{3x - 2}$

$let \: \: {f}^{ - 1} (x) = y$

$= > x = {2}^{3y - 2}$

$= > log_{2}(x) = 3y - 2$

$= > 3y = 2 + log_{2}(x)$

$= > y = \frac{2 + log_{2}(x) }{3}$

$= > {f}^{2} (x) = {2}^{6x - 4}$