Given the function f(x) = log4(x + 8), find the value of f^-1(2).

Solution:

A function is a process or a relation that associates each element 'a' of a non-empty set A , at least to a single element 'b' of another non-empty set B. A relation f from a set A (the domain of the function) to another set B (the co-domain of the function) is called a function in math. f = {(a,b)| for all a ∈ A, b ∈ B}

Given the function f(x) = log4(x + 8)

Let y = f(x) = log4(x + 8)

eʸ = 4(x + 8)

eʸ/4 = (x + 8)

eʸ/4 - 8 = x

y = f(x)

=> x = f⁻¹(y)

f⁻¹(2) = e² /4 - 8

= 2.25/4 - 8

= -7.43

Therefore, the value of f^-1(2) for the function f(x) = log4(x + 8) is -7.43

Given the function f(x) = log4(x + 8), find the value of f^-1(2).

Summary:

Given the function f(x) = log4(x + 8), the value of f^-1(2) is -7.43