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Question 392565: if f(x)=9x-5 what is f^-1(y)
Answer by haileytucki(390)   (Show Source):
You can put this solution on YOUR website! f(x)=9x-5_f^(-1)(y)
To find the inverse of the function, interchange the variables and solve for f^(-1)(x).
x=9f^(-1)(x)-5
Since f^(-1)(x) is on the right-hand side of the equation, switch the sides so it is on the left-hand side of the equation.
9f^(-1)(x)-5=x
Since -5 does not contain the variable to solve for, move it to the right-hand side of the equation by adding 5 to both sides.
9f^(-1)(x)=5+x
Move all terms not containing f^(-1)(x) to the right-hand side of the equation.
9f^(-1)(x)=x+5
Divide each term in the equation by 9.
(9f^(-1)(x))/(9)=(x)/(9)+(5)/(9)
Simplify the left-hand side of the equation by canceling the common factors.
f^(-1)(x)=(x)/(9)+(5)/(9)
Combine the numerators of all expressions that have common denominators.
f^(-1)(x)=(x+5)/(9)
Evaluate the inverse f^(-1) at x=y.
f^(-1)(y)=((y)+5)/(9)
Simplify the function.
f^(-1)(y)=(y+5)/(9)
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