The graph of a reciprocal function of the form f(x)=1/ax+b where a is not equal to 0 and b is not equal to 0.
Which is the equation of the original function f (x)?
a)y=5.25x-2
b)y=-5.25x+2
c)y=-5.25x-2
d)y=5.25x+2
To find the original function f(x) from the given reciprocal function f(x) = 1/(ax+b), we need to take the reciprocal of the given function.
Recalling that the reciprocal of a fraction is obtained by flipping it, we can find the reciprocal of f(x) = 1/(ax+b) by writing it as a single fraction and then flipping it:
f(x) = 1/(ax+b)
Reciprocal of f(x) = 1 / (1/(ax+b))
Reciprocal of f(x) = (ax+b)/1
Reciprocal of f(x) = ax+b
So, the equation of the original function f(x) is y = ax + b.
Now, let's compare the given answer choices with the equation of the original function:
a) y = 5.25x - 2
b) y = -5.25x + 2
c) y = -5.25x - 2
d) y = 5.25x + 2
Looking at the options, we can see that (d) y = 5.25x + 2 is the equation of the original function f(x). Therefore, the correct answer is option (d).