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3 years ago

Arithmetic of Functions problem.

Mathematics

2 answers:

FromTheMoon [43]3 years ago

5 0

Answer:

(f o g)(4) = 45

Step-by-step explanation:

We have given two functions and we have to find their composition.

f(x) = 4x+1 , g(x) = x²-5

Firstly, we have to find (f o g)(x)

Then, we have to find (f o g)(x).

(f o g)(x) = f(g(x))

Putting the given values of functions in above formula , we have

(f o g)(x) = f(x²-5)

(f o g)(x) = 4(x²-5)+1

simplifying

(f o g)(x) = 4x²-20+1

adding like terms, we have

(f o g)(x) = 4x²-19

Putting x = 4 to above equation , we have

(f o g)(4) = 4(4)²-19

(f o g)(4) = 4(16)-19

(f o g)(4) = 64-19

(f o g)(4) = 45 which is the answer.

lidiya [134]3 years ago

4 0

Answer:

(f o g)(4) = 45

Step-by-step explanation:

f(x)=4x+1

g(x)=x²-5

(f o g)(4)=?

(f o g)(4) = f(g(4))

Calculating g(4):

x=4→g(4)=4²-5

g(4)=16-5

g(4)=11

Replacing g(4)=11

(f o g)(4) = f(g(4))

(f o g)(4) = f(11)

Calculating f(11)

x=11→f(11)=4(11)+1

f(11)=44+1

f(11)=45

Replacing f(11)=45:

(f o g)(4) = f(11)

(f o g)(4) = 45

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Here's the question.

OleMash [197]

Answer:

The value of T₂₀ - T₁₅ is -20.

Step-by-step explanation:

Given :

>> If for an A.P, d = -4

To Find :

>> T₂₀ - T₁₅

Using Formula :

General term of an A.P.

$\star{\small{\underline{\boxed{\sf{\red{ T_n = a + (n - 1)d}}}}}}$

>> Tₙ = nᵗʰ term
>> a = first term
>> n = no. of terms
>> d = common difference

Solution :

Firstly finding the A.P of T₂₀ by substituting the values in the formula :

${\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}$

${\dashrightarrow{\sf{ T_{20} = a + (20 - 1) d}}}$

${\dashrightarrow{\sf{ T_{20} = a + (19)d}}}$

${\dashrightarrow{\sf{ T_{20} = a + 19 \times d}}}$

${\dashrightarrow{\sf{ T_{20} = a + 19d}}}$

${\star \: {\underline{\boxed{\sf{\pink{ T_{20} = a + 19d}}}}}}$

Hence, the value of T₂₀ is a + 19d.

$\rule{190}1$

Secondly, finding the A.P of T₁₅ by substituting the values in the formula :

${\dashrightarrow{\pmb{\sf{ T_n = a + (n - 1)d}}}}$

${\dashrightarrow{\sf{ T_{15}= a + (15 - 1) d}}}$

${\dashrightarrow{\sf{ T_{15}= a + (14) d}}}$

${\dashrightarrow{\sf{ T_{15}= a + 14 \times d}}}$

${\dashrightarrow{\sf{ T_{15}= a + 14d}}}$

${\star{\underline{\boxed{\sf \pink{ T_{15}= a + 14d}}}}}$

Hence, the value of T₁₅ is a + 14d

$\rule{190}1$

Now, finding the difference between T₂₀ - T₁₅ :

${\dashrightarrow{\pmb{\sf{T_{20} - T_{15}}}}}$

${\dashrightarrow{\sf{(a + 19d) - (a + 14d)}}}$

${\dashrightarrow{\sf{a + 19d - a - 14d}}}$

${\dashrightarrow{\sf{a - a + 19d - 14d}}}$

${\dashrightarrow{\sf{0+ 19d - 14d}}}$

${\dashrightarrow{\sf{19d - 14d}}}$

${\dashrightarrow{\sf{5 \times - 4}}}$

${\dashrightarrow{\sf{ - 20}}}$

${\star \: \underline{\boxed{\sf{\pink{T_{20} - T_{15} = - 20}}}}}$

Hence, the value of T₂₀ - T₁₅ is -20.

$\underline{\rule{220pt}{3.5pt}}$

3 0

2 years ago

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notka56 [123]

Answer:

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Step-by-step explanation:

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kotykmax [81]

We can create equations to solve this.

2.50p + 1.50m = 29.50
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Solve for a variable in the 2nd equation and use the substitution method to solve.

p + m = 15

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m = -p + 15

Plug in -p + 15 for m in the first equation.

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