The inverse of a linear function is always a linear function
The values of a, b, c and d could be 2, 3, 1 and 6
The functions are given as:
\(\mathbf{f(x) = x + ab}\)
\(\mathbf{g(x) = cx - d}\)
Assume that a = 2, and b = 3.
So, function f(x) becomes
\(\mathbf{f(x) = x + 2 \times 3}\)
\(\mathbf{f(x) = x + 6}\)
Represent f(x) with y
\(\mathbf{y = x + 6}\)
Swap the positions of x and y
\(\mathbf{x = y + 6}\)
Make y the subject
\(\mathbf{y = x - 6}\)
Express y as an inverse function
\(\mathbf{f^{-1}(x) = x - 6}\)
From the question, we understand that g(x) is an inverse function of f(x).
So, the function g(x) becomes
\(\mathbf{g(x) = x - 6}\)
By comparing \(\mathbf{g(x) = x - 6}\) and \(\mathbf{g(x) = cx - d}\)
\(\mathbf{c = 1}\) and \(\mathbf{d = 6}\)
Hence, the values of a, b, c and d could be 2, 3, 1 and 6
Read more about functions and inverses at:
https://brainly.com/question/10300045
