1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Tresset [83]
3 years ago
11

The function f(x)=(x-5)^2 +2 is not one-to-one. Identify a restricted domain that makes the function one-to-one, and find the in

verse function.
Mathematics
1 answer:
Anon25 [30]3 years ago
8 0

We have been given a quadratic function f(x)=(x-5)^{2} +2 and we need to restrict the domain such that it becomes a one to one function.

We know that vertex of this quadratic function occurs at (5,2).

Further, we know that range of this function is [2,\infty).

If we restrict the domain of this function to either (-\infty,5] or [5,\infty), it will become one to one function.

Let us know find its inverse.

y=(x-5)^{2}+2

Upon interchanging x and y, we get:

x=(y-5)^{2}+2

Let us now solve this function for y.

(y-5)^{2}=x-2\\
y-5=\pm \sqrt{x-2}\\
y=5\pm \sqrt{x-2}\\

Hence, the inverse function would be f^{-1}(x)=5+\sqrt{x-2} if we restrict the domain of original function to [5,\infty) and the inverse function would be f^{-1}(x)=5-\sqrt{x-2} if we restrict the domain to (-\infty,5].

You might be interested in
If g(x) = -4x + 5, find g(2x-1).
lilavasa [31]

Answer:

- 8x + 9

Step-by-step explanation:

To evaluate g(2x - 1) substitute x = 2x - 1 into g(x), that is

g(2x - 1)

= - 4(2x - 1) + 5 ← distribute parenthesis and simplify

= - 8x + 4 + 5

= - 8x + 9

8 0
3 years ago
Read 2 more answers
Find f(a), f(a+h), and<br> 71. f(x) = 7x - 3<br> f(a+h)-f(a)<br> h<br> if h = 0.<br> 72. f(x) = 5x²
Leni [432]

Answer:

71. \ \ \ f(a) \  = \  7a \ - \ 3; \ f(a+h) \  =  \ 7a \ + \ 7h \ - \ 3; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 7

72. \ \ \ f(a) \  = \  5a^{2}; \ f(a+h) \  =  \ {5a}^{2} \ + \ 10ah \ + \ {5h}^{2}; \ \displaystyle\frac{f(a+h) \ - \ f(a)}{h} \ = \ 10a \ + \ 5h

Step-by-step explanation:

In single-variable calculus, the difference quotient is the expression

                                              \displaystyle\frac{f(x+h) \ - \ f(x)}{h},

which its name comes from the fact that it is the quotient of the difference of the evaluated values of the function by the difference of its corresponding input values (as shown in the figure below).

This expression looks similar to the method of evaluating the slope of a line. Indeed, the difference quotient provides the slope of a secant line (in blue) that passes through two coordinate points on a curve.

                                             m \ \ = \ \ \displaystyle\frac{\Delta y}{\Delta x} \ \ = \ \ \displaystyle\frac{rise}{run}.

Similarly, the difference quotient is a measure of the average rate of change of the function over an interval. When the limit of the difference quotient is taken as <em>h</em> approaches 0 gives the instantaneous rate of change (rate of change in an instant) or the derivative of the function.

Therefore,

              71. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{(7a \ + \ 7h \ - \ 3) \ - \ (7a \ - \ 3)}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{7h}{h} \\ \\ \-\hspace{4.25cm} = \ \ 7

               72. \ \ \ \ \ \displaystyle\frac{f(a \ + \ h) \ - \ f(a)}{h} \ \ = \ \ \displaystyle\frac{{5(a \ + \ h)}^{2} \ - \ {5(a)}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{{5a}^{2} \ + \ 10ah \ + \ {5h}^{2} \ - \ {5a}^{2}}{h} \\ \\ \-\hspace{4.25cm} = \ \ \displaystyle\frac{h(10a \ + \ 5h)}{h} \\ \\ \-\hspace{4.25cm} = \ \ 10a \ + \ 5h

4 0
2 years ago
X/5 +8=3 what would x be
OverLord2011 [107]

Answer: x= -25

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Simplify to standard form<br> (2x +4) + (-7 – 3b) + (5 – 8x)
docker41 [41]

Answer:

−3b−6x+2

Step-by-step explanation:

2x+4−7−3b+5−8x

=2x+4+−7+−3b+5+−8x

Combine Like Terms:

=2x+4+−7+−3b+5+−8x

=(−3b)+(2x+−8x)+(4+−7+5)

=−3b+−6x+2

8 0
3 years ago
Kg=6x 1, gf=12x-5, and kf=32. what' is the value of x?
Elis [28]
<span>The answer is x = 2 
Hope this helps. </span>
4 0
3 years ago
Other questions:
  • Is -0.3 a rational number? is 3.14144144414444... a rational number?
    11·1 answer
  • n space you would fall with an acceleration of 9.8 m/s2. What would be your velocity after 6 seconds?
    13·1 answer
  • A motorcycle listed for 975$si sold for 820$ .what is the rate of discount that was allowed?​
    10·1 answer
  • Solve the differential equation by separation of variables<br> x(dy/dx)=4y
    6·1 answer
  • PLEASE HELP! (picture is shown) <br> which of the following points are collinear in this image?
    6·2 answers
  • Given R(3, 7,-1),S(10,-4,0) find an ordered triple that represents RS and find the magnitude of RS.
    13·2 answers
  • 0.33 (decimal) as a fraction in lowest term
    7·2 answers
  • 1 point
    7·2 answers
  • Kimberly sells handmade jewelry online, charging one price for bracelets and another price for necklaces. This table shows how m
    6·1 answer
  • Initial Knowledge CheckGoode Manufacturing pays Donald Sanchez a $590 monthly salary plus a 4% commission on merchandise he sell
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!