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Sphinxa [80]
3 years ago
7

Determine whether each pair of functions are inverse functions. Write yes or no.

Mathematics
1 answer:
Tatiana [17]3 years ago
6 0

Answer: No

Step-by-step explanation:

There are two ways to solve this. The first way is to calculate g(f(x)) (or f(g(x))). If f and g are inverse functions f(g(x)) = g(f(x)) = x.

g(f(x)) = (1/4)(2sqrt(x - 5))^2 - 5

= (1/4)*2^2*sqrt(x - 5)^2 - 5

= (1/4)*4*(x - 5) - 5

= x - 5 - 5

= x - 10

g(f(x)) = x - 10 =/= x, so the two functions are not inverse functions.

You can also solve this by using a test value a and calculating g(f(a)). If f and g are inverse functions, the result will be a.

For example, let a = 6.

f(6) = 2*sqrt(6 - 5)

= 2*sqrt(1)

= 2*1

= 1

g(f(6)) = g(1)

= (1/4)*1^2 - 5

= (1/4)*1 - 5

= 1/4 - 5

= -4 3/4

=/= 6

Therefore f and g are not inverse functions

Please note that this technique does not work in the other direction. If g(f(a)) = a, this does NOT prove that f and g are inverse functions.

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Solve.
Serggg [28]

Answer:

The solution is (4, 0)

Step-by-step explanation:

Using Linear combination method to solve:

2d + e = 8\\d - e = 4\\

Since "e" have the same coefficient in both equation with opposite operator; we will add.

(2d + d) + (e - e) = (8 + 4)\\3d = 12\\

Divide both side by coefficient of d which is 3

\frac{3d}{3}  = \frac{12}{3} \\d = 4\\

Since d = 4; put 'd' into any of the equation to get 'e'

2d + e = 8\\2(4) + e = 8\\8 + e = 8\\e = 8 - 8\\e = 0\\

Therefore, the solution is (4, 0)

5 0
3 years ago
Pelomyxa palustris is an amoeba with a length of 4.9 mm.Amoeba proteus has a length of 0.7 mm.How many amoeba proteus would you
prohojiy [21]

Answer:

  21

Step-by-step explanation:

Let n represent the number we're looking for. Then ...

  n × (proteus length) = 3 × (palustris length)

  n × 0.7 mm = 3 × 4.9 mm

  n = (3 × 4.9 mm)/(0.7 mm) = 3 × 49/7 = 3 × 7

  n = 21

You would have to line up 21 amoeba proteus to equal the length of three pelomyxa palustris.

3 0
3 years ago
What percentage describes the probability of an impossible event
stich3 [128]
50% chance
Explanation
It’s possible... might might not happen
7 0
3 years ago
For each scenario below, choose the graph that gives the best representation.
kvv77 [185]

The graph that gives the best representation of the scenario is: option 1 (A).

<h3>Graph of Distance vs Time</h3>
  • A typical graph of distance vs time shows the distance covered as against time.
  • If the graph shows a line that slopes upwards, it implies movement from a spot, if it shows an horizontal line, it implies a rest.

The first graph is the correct one that best represents the scenario because it starts at the point of origin (0, 0), which means the bird covers not distance at zero time when it is still at its nest.

As the bird flies, distance increases with time till it stopped at a point to eat.. This is represented by horizontal line, meaning time increased but distance from the nest remains the same.

The upward slope from the spot represents the further distance the bird is flying in search for more food.

Therefore, the graph that gives the best representation of the scenario is: option 1 (A).

Learn more about distance vs time graph on:

brainly.com/question/18655388

8 0
2 years ago
GUYS PLEASE HELP, 1 MILLION POINTS!!!
Salsk061 [2.6K]

Answer:

True

Step-by-step explanation:

8 0
3 years ago
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