Suppose that f(x)=4x+5. What is f^-1 (f^-1(9)) ?
Mathematics · Middle School · Sun Jan 24 2021
Answered on
Given the function:
f(x) = 4x + 5
Determine f^-1(f^-1(9))
Solution:
In order to determine the given condition, we must first solve for f^-1 or the inverse of the function. To solve for the inverse of the function, we equate f(x) to y, interchange the position of x, and y then solve for y. This can be shown as;
f(x) = 4x + 5
y = 4x + 5
x = 4y + 5
Transpose 5 to the other side of the equation, and divide both sides by 4. Note that in transposing a number, the sign changes.
4y = x - 5
4y/4 = (x - 5)/4
f^-1(x) = (x - 5)/4
Equate the value as,
f^-1(f^-1(9)) = ((9 - 5)/4 - 5)/4
f^-1(f^-1(9)) = ((4)/4 - 5)/4
f^-1(f^-1(9)) = (1 - 5)/4
f^-1(f^-1(9)) = (-4)/4
f^-1(f^-1(9)) = -1
Final answer:
f^-1(f^-1(9)) = -1