Proof that an invertible function f can have only one inverse
1 answer:
Step-by-step explanation:
We remeber that If we compose a function and it's inverse,
A invertible function is one to one so suppose that we have two inverse, g(x) and h(x). Let plug them in ,
and
Since f is a invertible function, it is one to one so if g and h are both inverse of f, then they are eqaul
Thus, a invertible function can have only one inverse.
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Answer:
The Slope Intercept form of the equation through the point (0, -4) and
(1, 0) is y = 4 x - 1
Step-by-step explanation:
Here, the given points are A (0,-4) and B(1,0)
Now, slope of the equation with points (a,b) and (c,d) is given as
So, here the slope of the line AB is given as:
⇒ m = 4
Now, by POINT SLOPE form:
The equation with slope m and point (x0 , y0) is represented as :
(y-y0) = m (x-x0)
⇒ The equation of AB is of the form with point (1,0) is
y - 0 = 4 (x -1)
or, y = 4 x - 1
Also, the SLOPE INTERCEPT form of an equation is of the form
y = m x + C ; m = slope and C = y -intercept
Hence, the slope intercept form of the equation through the point (0, -4) and (1, 0) is y = 4 x - 1