Find a symbolic representation for f^-1(x)
f(x)=8/x-5
Thanks
To find the inverse function, f^(-1)(x), we need to swap the roles of x and f(x) and solve for the new variable (in this case, x).
Given f(x) = 8 / (x - 5), let's replace f(x) with y:
y = 8 / (x - 5)
Now let's solve for x in terms of y:
Multiply both sides of the equation by (x - 5) to cancel out the denominator:
y * (x - 5) = 8
Expand the left side:
xy - 5y = 8
Rearrange the equation to solve for x:
xy = 8 + 5y
Divide both sides by y:
x = (8 + 5y)/y
Now we have the inverse function, f^(-1)(x), expressed in terms of x:
f^(-1)(x) = (8 + 5x)/x
Therefore, the symbolic representation for f^(-1)(x) is (8 + 5x)/x.