Question

Functions f and g are invertible functions.f(x) = 4x – 3 and g(2)1-2 +3Answer two questions about these functions.Write a simplified expression for f(g(x)) in terms of x.f(g(x)) =Are functions f and g inverses?19Choose 1 answer:АYesBNo

Answer 1

Given the two functions:

$\begin{gathered} f(x)=4x-3 \\ g(x)=\frac{1}{4}x+3 \end{gathered}$

To find f(g(x)):

$\begin{gathered} f(g(x))=f(\frac{1}{4}x+3)=4(\frac{1}{4}x+3)-3 \\ =x+12-3 \\ =x+9 \end{gathered}$

Since f(g(x)) is not equal to x, therefore the two functions are not inverse of each other.