Ans: The inverse of the function is = [tex]f^{-1}(x)[/tex] = [tex] \frac{ln(x-6)}{ln(2)} [/tex]
Explanation:
Given function:
f(x) = 2^x + 6
Step 1:
We can write f(x) as y:
y = 2^x + 6
Step 2:
Interchange x with y and vice versa:
x = 2^y + 6
Step 3:
Now solve for y:
x - 6 = 2^y
Take "ln" (natural log) on both sides:
ln(x-6) = ln(2^y)
ln(x-6) = yln(2)
y = [tex] \frac{ln(x-6)}{ln(2)} [/tex]
Step 4:
Now replace y with [tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(x)[/tex] = [tex] \frac{ln(x-6)}{ln(2)} [/tex]
