Find the inverse of the following function. g(x)= 1/x - 4
Show all steps.
A. g^-1(x)= - 2/x-1
B. g^-1(x)= 1/x+4**
C. g^-1(x)= 1/x+ 2
D. g^-1(x)= 2/x+1
I have the answer, but not the steps.
that would be 1/(x+4)
Parentheses matter
change variables:
x = 1/y - 4
solve for the new y:
x+4 = 1/y
y = 1/(x+4)
Hi
To find the inverse of a function, we need to switch the roles of x and y and solve for y. In other words, we need to solve the equation x = 1/y - 4 for y.
Step 1: Switch x and y in the original equation:
x = 1/y - 4
Step 2: Add 4 to both sides of the equation:
x + 4 = 1/y
Step 3: Take the reciprocal of both sides of the equation:
1/(x + 4) = y
So, the inverse of the function g(x) = 1/x - 4 is g^(-1)(x) = 1/(x + 4).
Comparing this result with the given options, we can see that option B, g^(-1)(x) = 1/(x + 4), is the correct answer.