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Contact [7]
4 years ago
10

For the function f(x)=

rac{\sqrt{x} }{5} +2" alt="\frac{\sqrt{x} }{5} +2" align="absmiddle" class="latex-formula">
A. ƒ –1(x) = 25(x – 2)2, x ≥ 2

B. ƒ –1(x) = 25x2 – 2, x ≥ 0

C. ƒ –1(x) = 5(x – 2)2, x ≥ 0

D. ƒ –1(x) = 25(x – 2)2, x ≥ 0

Mathematics
1 answer:
Ber [7]4 years ago
4 0

Answer:

f^{-1}(x)=25(x-2)^2

Step-by-step explanation:

The inverse function can be found by solving ...

  f(y) = x

  (√y)/5 +2 = x

  (√y)/5 = x -2 . . . . . subtract 2

  √y = 5(x -2) . . . . . . multiply by 5

  y = 25(x -2)² . . . . . square both sides

The inverse function is ...

  f^{-1}(x)=25(x-2)^2

_____

<em>About the graph</em>

The inverse of a function is its mirror image across the line y = x.

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7 0
3 years ago
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Mathieu is finding the x-intercepts of the function f(x)=x^2+4x+3. His world is shown below. (In the photo) The Answer is: (He s
navik [9.2K]

Answer:

X intercepts are points where a function intersects or cuts through the x axis where y=0.

Step-by-step explanation:

In the function given which is f(x) =x^2 +4x + 3 we see that this is a parabola of which when the graph is drawn it has a U shape so when finding x intercepts of this function it is those points on the function where the graph cuts the x axis and at those two points f(x)= 0, so here Mathieu had made a mistake of factorizing and equating the x intercepts for this function.

For finding the X intercepts let f(x) = 0

therefore 0= x^2 + 4x + 3  now we solve for x

0= (x+1)(x+3)  

(x+1)= 0 or (x+3)=0

therefore x=-1 or x=-3

now if you substitute these values onto the function they give f(x)= 0,

f(-1) = (-1)^2 + 4(-1) + 3 = 0

f(-3) = (-3)^2 + $(-3) + 3 =0

now let us look at Mathieus answer which is x+1 = x+3 yes these x values do give the same y value but they are not equal because if you can actually solve this further you would not get a defined answer. Both these are factors of the function but are not actually equal as the function would not be able to be drawn if this was the case.

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3 years ago
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Solve this quadratic equation using the quadratic formula. 2x2 - 10x + 7 = 0
irina [24]

Answer:

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Decimal Form: x = 4.15

3 0
3 years ago
The regression equation y=0.5x+1.3 approximates the number of hours it takes to arrange a dinner event, y, given the number of p
Sphinxa [80]

It would be C.

For example, say 1 person comes. This would be x=1. Plugging this in gives you,

y=0.5 + 1.3

This shows that C is true since x is always going to be multiplied by 0.5.

1.3 would be the base amount of time it takes to arrange since if it the y-intercept.


5 0
3 years ago
Determine the volume of a cylindrical bucket if the diameter is 8.5 in. and the height is 11.5 in.
steposvetlana [31]
Volume=heiht times area of base
base=circle
area of circle=pir^2

volume=hpir^2

diameter=2r
diametr/2=r
diameter=8.5
find radius
r=8.5/2
r=4.25

h=11.5
subsitute

v=11.5 times pi times 4.25^2
v=11.5 times pi times 18.0625
v=pi times 207.71875
round to hundreth
v=207.72pi in^3

volue=207.72pi in^3
if you want to aprox pi to 3.14 and solve for that then
v=207.72 times 3.14
v=652.24



so
v=207.72pi in^3 or
v=652.24 in^3 aprox (both aer eequatal)
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