02.08.2022

If f(x) = x-1 and g(x) = 2x, what is and g(f(x))

. 1

Step-by-step answer

09.07.2023, solved by verified expert

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Mathematics
Step-by-step answer
P Answered by PhD

\frac{3}{4}

The composition of a function is a process in which two functions f,g, are combined to produce a new function, h, with the formula h(x)=g(f(x)). It means that the g function is being applied to the x function.

f(x)=x-1\\g(x)=2x^2+3

f(g(x))=f(2x^2+3)

            =2x^2+3-1\\=2x^2+2

g(f(x))=g(x-1)

           =2(x-1)^2+3\\=2x^2+2-4x+3\\=2x^2-4x+5

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

2x^2+2=2x^2-4x+5

       4x=3

        x=\frac{3}{4}

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Mathematics
Step-by-step answer
P Answered by PhD

\frac{3}{4}

The composition of a function is a process in which two functions f,g, are combined to produce a new function, h, with the formula h(x)=g(f(x)). It means that the g function is being applied to the x function.

f(x)=x-1\\g(x)=2x^2+3

f(g(x))=f(2x^2+3)

            =2x^2+3-1\\=2x^2+2

g(f(x))=g(x-1)

           =2(x-1)^2+3\\=2x^2+2-4x+3\\=2x^2-4x+5

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

2x^2+2=2x^2-4x+5

       4x=3

        x=\frac{3}{4}

For more information:

link

Mathematics
Step-by-step answer
P Answered by Specialist

f(g(x)) =  2x - 1

Step-by-step explanation:

learn composite functions

Mathematics
Step-by-step answer
P Answered by PhD

f(x) = x - 1

g(x) = 2x

To compute g(f(x)), replace every instance of x in the definition of g(x) with f(x). This would given you

g(f(x)) = g (x - 1) = 2 (x - 1) = 2x - 2

Mathematics
Step-by-step answer
P Answered by PhD
We have the following functions:
 f (x) = x-1
 g (x) = 2x-3

 For the sum we have:
 f (x) + g (x) = (x-1) + (2x-3)
 f (x) + g (x) = 3x - 4

 For subtraction we have:
 f (x) - g (x) = (x-1) - (2x-3)
 f (x) - g (x) = -x + 2

 For  the product we have:
 f (x) * g (x) = (x-1) * (2x-3)
 f (x) * g (x) = 2x ^ 2 - 3x - 2x + 3
 f (x) * g (x) = 2x ^ 2 - 5x + 3

 For the quotient we have:
 f (x) / g (x) = (x-1) / (2x-3)
Mathematics
Step-by-step answer
P Answered by PhD
We have the following functions:
 f (x) = x-1
 g (x) = 2x-3

 For the sum we have:
 f (x) + g (x) = (x-1) + (2x-3)
 f (x) + g (x) = 3x - 4

 For subtraction we have:
 f (x) - g (x) = (x-1) - (2x-3)
 f (x) - g (x) = -x + 2

 For  the product we have:
 f (x) * g (x) = (x-1) * (2x-3)
 f (x) * g (x) = 2x ^ 2 - 3x - 2x + 3
 f (x) * g (x) = 2x ^ 2 - 5x + 3

 For the quotient we have:
 f (x) / g (x) = (x-1) / (2x-3)
Mathematics
Step-by-step answer
P Answered by Master

C) f(x) x g(x) = 6x2 + x-1

Step-by-step explanation:

Multiplication of functions:

Two multiply two polynomial functions, we apply the distributive property(multiply each two terms and add).

In this question, we have that:

f(x) = 3x - 1, g(x) = 2x + 1

The multiplication is:

f(x) \times g(x) = (3x - 1)(2x+1) = 3x*2x + 3x*1 -1*2x -1*1 = 6x^2 + 3x - 2x - 1 = 6x^2 + x - 1

The correct answer is given by option C.

Mathematics
Step-by-step answer
P Answered by Master

C) f(x) x g(x) = 6x2 + x-1

Step-by-step explanation:

Multiplication of functions:

Two multiply two polynomial functions, we apply the distributive property(multiply each two terms and add).

In this question, we have that:

f(x) = 3x - 1, g(x) = 2x + 1

The multiplication is:

f(x) \times g(x) = (3x - 1)(2x+1) = 3x*2x + 3x*1 -1*2x -1*1 = 6x^2 + 3x - 2x - 1 = 6x^2 + x - 1

The correct answer is given by option C.

Mathematics
Step-by-step answer
P Answered by PhD
C. 5x - 1

Step-by-step explanation:

Givenf(x) = 3x-2 and g(x) = 2x+1To find (f+g)(x)Solution(f+g)(x) =f(x) + g(x) =3x - 2 + 2x + 1 =5x - 1
Mathematics
Step-by-step answer
P Answered by PhD
G(x)=2x+1
f(2x+1)=3(2x+1)-2
6x+3-2=6x-1
Sorry this was the answer that I had 6x-1
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