make x the subject of the formula
y=2x+3
x-4
hence determine the inverse of f(x) for the equation where x is not equal to 4
I presume you mean
y = (2x+3)/(x-4)
In that case,
xy-4y = 2x+3
x(y-2) = 4y+3
x = (4y+3)/(y-2)
so, f-1(x) = (4x+3)/(x-2)
To make x the subject of the formula y=2x+3, we can follow these steps:
Step 1: Start with the equation: y = 2x + 3
Step 2: Subtract 3 from both sides to isolate the 2x term: y - 3 = 2x
Step 3: Divide both sides by 2 to solve for x: (y - 3) / 2 = x
Therefore, x = (y - 3) / 2.
Now, to determine the inverse of f(x), we need to switch the roles of x and y and solve for y.
Step 4: Replace x with y and y with x: x = (y - 3) / 2
Step 5: Multiply both sides by 2 to isolate y: 2x = y - 3
Step 6: Add 3 to both sides to solve for y: y = 2x + 3.
So, the inverse of f(x) is given by f^(-1)(x) = 2x + 3.
To make x the subject of the formula, we need to isolate x on one side of the equation. Let's start with the equation:
1. y = 2x + 3
To do this, we'll need to perform some algebraic operations to move the terms around. Here's how:
Step 1: Subtract 3 from both sides of the equation:
y - 3 = 2x
Step 2: Divide both sides of the equation by 2:
(y - 3) / 2 = x
Now, we have x as the subject of the formula:
x = (y - 3) / 2
Now, to determine the inverse of f(x), we need to swap the positions of x and y in the equation. Let's call the inverse function g(x):
2. g(x) = (x - 3) / 2
However, remember that x cannot be equal to 4 for this inverse function because the original function had the restriction x ≠ 4. So, the final inverse function is:
g(x) = (x - 3) / 2, where x ≠ 4