Answer:
f⁻¹(x) = [tex]2^{\dfrac{x}{4} }[/tex] + 7
Step-by-step explanation:
The inverse of a function reverses the operations performed by the function in the question such if f(x) = y, then we have, f⁻¹(y) = x, which reverses the operation of the first function.
The inverse of a function f(x) = 4·㏒₂(x - 7) is found as follows;
We have;
y = 4·㏒₂(x - 7)
We substitute x for y to get;
x = 4·㏒₂(y - 7) which gives;
x/4 = ㏒₂(y - 7)
[tex]2^{\dfrac{x}{4} }[/tex] = y - 7
y = [tex]2^{\dfrac{x}{4} }[/tex] + 7
Therefore;
f⁻¹(x) = [tex]2^{\dfrac{x}{4} }[/tex] + 7.
