SOLUTION: If f(x) =-10x - 6, what is f -1(x)?

Question 1073268: If f(x) =-10x - 6, what is f -1(x)?
Found 2 solutions by Fombitz, Theo:
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!

Interchange x and y and solve for the new y, that's the inverse.

Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
you are looking for the inverse function.

let y = f(x).

your equation becomes y = -10x - 6

replace y with x and x with y and then solve for y.

replacing y with x and x with y gets you x = -10y - 6

solve this equation for y as follows:

start with x = -10y - 6

add 6 to both sides to get x + 6 = -10y

divide both sides by -10 to get y = (x + 6) / -10

if this is the inverse equation, then the point (x,y) in the original equation will be equal to the point (y,x) in the inverse equation.

to confirm that, let x be any value and then solve for y in the original equation.

for example, let x = 1 in the original equation.

y = -10x - 6 becomes y = -10 * 1 - 6 which becomes y = -10 - 6 which becomes y = -16.

your coordinate point from the first equation is (1,-16).

the corresponding coordinate point in the inverse equation will be (-16,1).

your inverse equation is y = (x+6)/-10.

replace x with -16 and you get y = (-16 + 6)/ -10.

simplify to get y = -10 / -10.

solve for y to get y = 1.

your corresponding point in the inverse equation is (-16,1).

(x,y) in the original equation becomes (y,x) in the inverse equation.

(1,-16) in the original equation becomes (-16,1) in the inverse equation.

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