Question
Find the inverse of the function.
y = –3 over x + 4
A. x = 4y – 3 over y
B. y = 4x over 3
C. y = x –3 over x
D. y = –4x –3 over x
y = –3 over x + 4
A. x = 4y – 3 over y
B. y = 4x over 3
C. y = x –3 over x
D. y = –4x –3 over x
Asked by: USER3524
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Answer (175)
[tex]y= \frac{-3}{x+4} [/tex]
Step 1: Isolating x on one side of the equation.
[tex]y(x+4)=-3 \\ \\ x+4= \frac{-3}{y} \\ \\ x= \frac{-3}{y}-4 [/tex]
Step 2: Replace x by f'(y)
[tex]f'(y)= \frac{-3}{y}-4 [/tex]
Step 3: Replace each occurrence of y by x
[tex]f'(x)= \frac{-3}{x}-4 \\ \\ f'(x)= \frac{-3-4x}{x} [/tex]
Thus, option D gives the correct inverse of the given function
Step 1: Isolating x on one side of the equation.
[tex]y(x+4)=-3 \\ \\ x+4= \frac{-3}{y} \\ \\ x= \frac{-3}{y}-4 [/tex]
Step 2: Replace x by f'(y)
[tex]f'(y)= \frac{-3}{y}-4 [/tex]
Step 3: Replace each occurrence of y by x
[tex]f'(x)= \frac{-3}{x}-4 \\ \\ f'(x)= \frac{-3-4x}{x} [/tex]
Thus, option D gives the correct inverse of the given function