Question

What is the inverse relation of thr function f(x) = -7/2x+4

Answer 1

The inverse of the function is $y=-\frac{2}{7} x+\frac{8}{7}$

Explanation:

The given function is $f(x)=-\frac{7}{2} x+4$

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,

$x=-\frac{7}{2} y+4$

Now, we shall solve for y

Subtracting both sides of the equation by 4, we get,

$x-4=-\frac{7}{2} y$

Multiplying both sides of the equation by $-\frac{2}{7}$, we get,

$-\frac{2}{7} (x-4)= y$

Switch sides, we have,

$y=-\frac{2}{7} (x-4)$

Multiplying the terms within the bracket, we have,

$y=-\frac{2}{7} x+\frac{8}{7}$

Thus, the inverse of the function is $y=-\frac{2}{7} x+\frac{8}{7}$