If f(x)=5x-25 and g(x)=1/5x+5, which expression could be used to verify g(x) is the inverse of f(x)?
Mathematics · Middle School · Mon Jan 18 2021
Answered on
Given the function:
f(x) = 5x - 25
g(x) = 1/5x + 5
Determine the inverse of the function to verify if g(x) is equal to the inverse of f(x).
Solution:
In order to change the inverse of the function, we simply need to equate f(x) to y, then interchange the position of y and x, then solve for y.
f(x) = 5x - 25
y = 5x - 25
x = 5y - 25
Transpose -25 on the other side of the equation, hence it must be taken to note that in transposing a number, the sign changes.
5y = x + 25
Divide both sides by 5 in order to cancel out 5y, leaving behind y.
5y/5 = ( x + 25 ) /5
y= 1/5x + 5
f^-1(x) = 1/5x + 5
Final answer:
g(x) is the inverse of f(x).