if f(x) and f^-1(x) are inverse functions of eachother and f(x)=2x+5, what is f^-1(8)
Mathematics · High School · Mon Jan 18 2021
Answered on
Given the function:
f(x) = 2x + 5
Determine f^-1(8)
Solution:
Convert first the given function into an inverse function. This can be done by equating f(x), as y, and then substituting the positions of x and y. Lastly, we solve for y.
f(x) = 2x + 5
y = 2x + 5
x = 2y + 5
Transpose 5 on the other side of the equation, hence it must be taken to note than when transposing a number, the sign changes.
2y = x - 5
Divide both sides by 2 in order to cancel out y.
2y/2 = ( x - 5)/2
f^-1(x) = ½x - 5/2
f^-1(8) = ½(8) - 5/2
f^-1(8) = 8/2 - 5/2
f^-1(8) = 3/2
Final answer:
f^-1(8) = 3/2