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Licemer1 [7]
2 years ago
8

Proof that an invertible function f can have only one inverse

Mathematics
1 answer:
True [87]2 years ago
8 0

Step-by-step explanation:

We remeber that If we compose a function and it's inverse,

f(f {}^{ - 1} x) = x

A invertible function is one to one so suppose that we have two inverse, g(x) and h(x). Let plug them in ,

f(h(x)

and

f(g(x)

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

f(h(x) = f(g(x)

h(x) = g(x)

Thus, a invertible function can have only one inverse.

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Can somebody help me with the rest of the question
kari74 [83]

Shop #1 has the best price for 21 pizzas because it is $105, while Shop #2 costs $147 for 21 pizzas which is a lot more money. they would save $42, which is 147-105=42. hope this helps:)

5 0
3 years ago
Find the slope-intercept form of the equation of the line through the point (0, -4) and (1, 0).
Arisa [49]

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

m = \frac{d - b}{c -a}

So, here the slope of the line AB is given as:

m = \frac{0 - (-4)}{1-0} = \frac{4}{1}  = 4

⇒ 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

4 0
3 years ago
Triangle GCH is similar to triangle DCE. Find CH
soldier1979 [14.2K]

Answer:

x = 65

Step-by-step explanation:

if two triangles are similar then we can use the similarity ratio to find the length of CH

60/156 = x/169 cross multiply expressions

156x = 10140 divide both sides by 156

x = 65

5 0
3 years ago
A rectangular solid has a base with length 2 centimeters and a width of 8 centimeters. If the volume of the solid is 160 centime
Whitepunk [10]
10 centimeters it is 160/8=20/2=10
8 0
3 years ago
What is 12 2/3 as an improper fraction
BaLLatris [955]

Answer:

\dfrac{38}{3}

Step-by-step explanation:

12\dfrac{2}{3} =

= 12 + \dfrac{2}{3}

= \dfrac{12}{1} + \dfrac{2}{3}

= \dfrac{12}{1} \times \dfrac{3}{3} + \dfrac{2}{3}

= \dfrac{36}{3} + \dfrac{2}{3}

= \dfrac{38}{3}

4 0
3 years ago
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