Question

If ( f(x) = 4x-3 ), which of the following is the inverse of ( A(x) )?

a) ( F'(x) = 7x-2 )
b) ( F'(x) = 4x - 3 )
c) ( F(x) = 742 )
d) ( F'(x) = 4x + 3 )

Answer 1

To find the inverse of the function f(x) = 4x - 3, we swap the x and y variables and solve for y. The correct inverse function would be F'(x) = (x + 3) / 4. However, none of the options provided exactly match this function.

Step-by-step explanation:

To find the inverse of a function, f(x), we need to swap the x and y variables and then solve for y. The given function is f(x) = 4x - 3.

Step 1: Replace f(x) with y:
y = 4x - 3

Step 2: Swap x and y:
x = 4y - 3

Step 3: Solve for y:
x + 3 = 4y
y = (x + 3) / 4

Therefore, the inverse function, F'(x), should be F'(x) = (x + 3) / 4. None of the options given exactly match this function, but if we are to assume a typo and that (d) F'(x) = 4x + 3 was meant to express the inverse correctly, then (d) would be the closest choice with a mistake in the presentation of the coefficient.