Find the inverse of the following function. g(x)=1x−4 (1 point) Responses g−1(x)=−2x−1 g inverse of x is equal to negative the fraction with numerator 2 and denominator x minus 1 g−1(x)=1x+2 g inverse of x is equal to the fraction with numerator 1 and denominator x plus 2 g−1(x)=2x+1 g inverse of x is equal to the fraction with numerator 2 and denominator x plus 1 g−1(x)=1x+4

Question

Find the inverse of the following function. g(x)=1x−4 (1 point) Responses g−1(x)=−2x−1 g inverse of x is equal to negative the fraction with numerator 2 and denominator x minus 1 g−1(x)=1x+2 g inverse of x is equal to the fraction with numerator 1 and denominator x plus 2 g−1(x)=2x+1 g inverse of x is equal to the fraction with numerator 2 and denominator x plus 1 g−1(x)=1x+4

Answer 1

To find the inverse of the function g(x) = 1x - 4, we can follow these steps:

Step 1: Replace g(x) with y.
y = 1x - 4.

Step 2: Swap the variables x and y.
x = 1y - 4.

Step 3: Solve the equation for y.
x + 4 = 1y.
y = x + 4.

Therefore, the inverse of the function g(x) = 1x - 4 is g^(-1)(x) = x + 4.