The inverse of the function is [tex]y=-\frac{2}{7} x+\frac{8}{7}[/tex]
Explanation:
The given function is [tex]f(x)=-\frac{7}{2} x+4[/tex]
To determine the inverse of a function, we need to interchange the variables and solve for y.
Let us interchange the variables x and y
Thus, we have,
[tex]x=-\frac{7}{2} y+4[/tex]
Now, we shall solve for y
Subtracting both sides of the equation by 4, we get,
[tex]x-4=-\frac{7}{2} y[/tex]
Multiplying both sides of the equation by [tex]-\frac{2}{7}[/tex], we get,
[tex]-\frac{2}{7} (x-4)= y[/tex]
Switch sides, we have,
[tex]y=-\frac{2}{7} (x-4)[/tex]
Multiplying the terms within the bracket, we have,
[tex]y=-\frac{2}{7} x+\frac{8}{7}[/tex]
Thus, the inverse of the function is [tex]y=-\frac{2}{7} x+\frac{8}{7}[/tex]
