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Masja [62]
2 years ago
14

If f ( x ) = x 4 + 6 , g ( x ) = x − 5 and h ( x ) = √ x , then f ( g ( h ( x ) ) ) =

Mathematics
1 answer:
zaharov [31]2 years ago
3 0

Answer:

fgh(x)=4\sqrt{x} -14

Step-by-step explanation:

when solving composite fuctions we go from the right to the left

meaning we replace the x in the g function with the entire h function

then replace the x in the f function with the entire new g function

h(x)=\sqrt{x}

g(\sqrt{x})=\sqrt{x} -5

f(\sqrt{x}-5)=4(\sqrt{x} -5)+6

f(\sqrt{x}-5)=4\sqrt{x} -20+6

fgh(x)=4\sqrt{x} -14

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If y varies directly with x, and y is 6
Dvinal [7]

Answer:

12

Step-by-step explanation:

see the pic for the steps

6 0
3 years ago
Which is one of the transformations applied to the graph of f(x)=x2 to change it into the graph of g(x) = -x2 + 16x – 44?
KatRina [158]

Answer:

Only option D is one of the transformations needed.

Step-by-step explanation:

The graph of f(x)=x^2 is a positive parabola with x=0 as the zero in ordinates and also 0 as a zero x. This is, the graph passes in (0,0) and this is the only point it crosses both axis, then for every x value we will gave a positive f(x).

Here I attach a graph that shows both, f(x)=x^2 and g(x)=-x^2+16x-44.

As you can see, for transforming f(x) in g(x) we need to reflect it over the x axis, as g is open downwards. Then, as the quadratic term is still being x^2 we do not wide it (as you see in the graph both curves are equally widened).

Then, we can also see that the graph is shifted right, so we do not shift it left 8 units (notice that we shift it right 8 units).

So, after reflecting over the x axis and shifting right we need to shift it UP, as we can see the graph is over the x axis.

So, the three transformations needed are:

1. reflect over the x axis

2. shift right 8 units

3. shift up 20 units.

So, from the options you proposed we chose only d, to which we MUST add the transformations noted above.

Sorry for the mistake!

8 0
3 years ago
Read 2 more answers
Each person in a group of college students was identified by graduating year and asked when he or she preferred taking classes:
swat32

Answer:

<em>0.615</em>

Step-by-step explanation:

The frequency table is attached below.

We have to calculate, the probability that the student preferred morning classes given he or she is a junior.

i.e P(\text{Morning }|\text{ Junior})

We know that,

P(A\ |\ B)=\dfrac{P(A\ \cap\ B)}{P(B)}

So,

P(\text{Morning }|\text{ Junior})=\dfrac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}

Putting the values from the table,

\dfrac{P(\text{Morning }\cap \text{ Junior})}{P(\text{Junior})}=\dfrac{\frac{16}{143}}{\frac{26}{143}}=\dfrac{16}{26}=0.615

3 0
3 years ago
WILL GIVE BRAINLIEST!!!! it looks like an explanation but i just need an answer!!
Slav-nsk [51]

Answer:

5: 60

6: 30

Step-by-step explanation:

just a matter of multiplying all the possible values

5: 5 pants X 4 shirts X 3 shoes

6: 10 numbers (0-9) X 3 variations (right, left, right,)

5 0
3 years ago
It took Jean 1/2 hour to complete 3/8 of a math problem
skad [1K]
Ok, if you say so. Jean took 1/2 hour to complete 3/8 of a math problem.


8 0
3 years ago
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