Question

I need steps to find the equation of the inverse of the function f(x) = log2 (9x).

Answer 1

Answer:

f⁻¹(x) = 2ˣ / 9

Step-by-step explanation:

f(x) = log₂ (9x)

y = log₂ (9x)

swap y and x:    x = log₂ (9y)

solve y: 9y = 2ˣ        y = 2ˣ / 9

f⁻¹(x) = 2ˣ / 9

Answer 2

The equation of the inverse of the function f(x) = log2 (9x) should be considered as the $f^{-1}(x) = 2^x / 9$

Calculation of the equation of the inverse of the function:

Since

f(x) = log₂ (9x)

So,

y = log₂ (9x)

Now

swap y and x so    x = log₂ (9y)

And, now we have to solve for y

9y = 2ˣ      

y = 2ˣ / 9

f⁻¹(x) = 2ˣ / 9

Hence, The equation of the inverse of the function f(x) = log2 (9x) should be considered as the $f^{-1}(x) = 2^x / 9$

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