Composition Of Functions Questions And Answers

1) Find the value of f(6) in f(x)=x²+3x-2

To find the value of f(6), we substitute 6 into the function f(x)=x²+3x-2. Plugging in 6 for x, we get f(6)=6²+3(6)-2. Simplifying this expression, we have f(6)=36+18-2=52. Therefore, the value of f(6) is 52.

Explanation

To find the value of f(6), we substitute 6 into the function f(x)=x²+3x-2. Plugging in 6 for x, we get f(6)=6²+3(6)-2. Simplifying this expression, we have f(6)=36+18-2=52. Therefore, the value of f(6) is 52.

Submit

2) Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f/g.

F/g= (3x+1) /(7+2x)

F/g= (3x+½) /(7+2x)

F/g= (3x+½) /(6+2x)

F/g= (3x-1) /(7+2x)

The given correct answer for f/g is (3x+1) /(7+2x). This is obtained by substituting the given functions f(x) = 3x+1/2 and g(x) = 7+2x into the expression f/g. By dividing the numerator (3x+1) by the denominator (7+2x), we get the desired result.

Explanation

The given correct answer for f/g is (3x+1) /(7+2x). This is obtained by substituting the given functions f(x) = 3x+1/2 and g(x) = 7+2x into the expression f/g. By dividing the numerator (3x+1) by the denominator (7+2x), we get the desired result.

3) Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f+g.

F+g=5x+7 ½

F+g=x+7 ½

F+g=5x+7

F+g=5x-7 ½

The given functions are f(x) = 3x+1/2 and g(x) = 7+2x. To find f+g, we need to add the two functions together. When we add the two functions, we add the coefficients of x and the constant terms separately. So, for the x term, we have 3x + 2x = 5x. For the constant terms, we have 1/2 + 7 = 7 1/2. Therefore, f+g = 5x + 7 1/2.

Explanation

The given functions are f(x) = 3x+1/2 and g(x) = 7+2x. To find f+g, we need to add the two functions together. When we add the two functions, we add the coefficients of x and the constant terms separately. So, for the x term, we have 3x + 2x = 5x. For the constant terms, we have 1/2 + 7 = 7 1/2. Therefore, f+g = 5x + 7 1/2.

4) Given functions f(x) = 3x+½ and g(x)= 7+2x. Find g ∘ f.

G ∘ f=6x+8

G ∘ f=6x+9

G ∘ f=x+8

G ∘ f=x-8

The composition of functions g ∘ f means that the output of function f is used as the input for function g. In this case, function f multiplies the input by 3 and adds 1/2, and function g multiplies the input by 2 and adds 7. Therefore, when we substitute f(x) into g(x), we get g ∘ f = 2(3x+1/2) + 7 = 6x + 1 + 7 = 6x + 8.

Explanation

The composition of functions g ∘ f means that the output of function f is used as the input for function g. In this case, function f multiplies the input by 3 and adds 1/2, and function g multiplies the input by 2 and adds 7. Therefore, when we substitute f(x) into g(x), we get g ∘ f = 2(3x+1/2) + 7 = 6x + 1 + 7 = 6x + 8.

5) For f(x) = 2x + 3 and g(x) = -x² + 1, find (f _o g)(x)

- 2x2+5

2x2+5

- 2x2+7

- 2x2-5

The function (f o g)(x) represents the composition of functions f and g. To find (f o g)(x), we first substitute g(x) into f(x).

g(x) = -x^2 + 1

Substituting g(x) into f(x):

f(g(x)) = 2(-x^2 + 1) + 3
= -2x^2 + 2 + 3
= -2x^2 + 5

Therefore, the correct answer is -2x^2 + 5.

Explanation

The function (f o g)(x) represents the composition of functions f and g. To find (f o g)(x), we first substitute g(x) into f(x).

g(x) = -x^2 + 1

Substituting g(x) into f(x):

f(g(x)) = 2(-x^2 + 1) + 3
= -2x^2 + 2 + 3
= -2x^2 + 5

Therefore, the correct answer is -2x^2 + 5.

6) Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f-g.

F(x)=x-6½

F(x)=x-5½

F(x)=2x-6½

F(x)=x+6½

The given functions are f(x) = 3x + 1/2 and g(x) = 7 + 2x. To find f-g, we subtract the two functions.

Subtracting g(x) from f(x), we get (3x + 1/2) - (7 + 2x).

Simplifying the expression, we combine like terms: 3x - 2x + 1/2 - 7.

This further simplifies to x - 6 1/2, which matches the answer choice f(x) = x - 6 1/2.

Explanation

The given functions are f(x) = 3x + 1/2 and g(x) = 7 + 2x. To find f-g, we subtract the two functions.

Subtracting g(x) from f(x), we get (3x + 1/2) - (7 + 2x).

Simplifying the expression, we combine like terms: 3x - 2x + 1/2 - 7.

This further simplifies to x - 6 1/2, which matches the answer choice f(x) = x - 6 1/2.

7) Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f ∘ g.

F ∘ g= 7x+21 ½

F ∘ g= 6x+21

F ∘ g= 6x+21 ½

None of these

The composition of functions f ∘ g is found by substituting the expression for g(x) into f(x). In this case, g(x) = 7 + 2x. Substituting this into f(x) = 3x + 1/2 gives f ∘ g = 3(7 + 2x) + 1/2 = 21 + 6x + 1/2 = 6x + 21 1/2. Therefore, the correct answer is f ∘ g = 6x + 21 1/2.

Explanation

The composition of functions f ∘ g is found by substituting the expression for g(x) into f(x). In this case, g(x) = 7 + 2x. Substituting this into f(x) = 3x + 1/2 gives f ∘ g = 3(7 + 2x) + 1/2 = 21 + 6x + 1/2 = 6x + 21 1/2. Therefore, the correct answer is f ∘ g = 6x + 21 1/2.

8) Given functions f(x) = 3x+½ and g(x)= 7+2x. Find fmg.

F(x)=6x²+21x+2½

F(x)=6x²+22x+3½

F(x)=5x²+20x+2½

None of these

The given functions are f(x) = 3x+½ and g(x)= 7+2x. To find f×g, we need to substitute g(x) into f(x). Substituting g(x) into f(x), we get f×g = f(g(x)) = f(7+2x). Simplifying this expression, we get f×g = 3(7+2x)+½. Expanding and simplifying further, we get f×g = 21+6x+½. So, the correct answer is f(x)=6x²+22x+3½.

Explanation

The given functions are f(x) = 3x+½ and g(x)= 7+2x. To find f×g, we need to substitute g(x) into f(x). Substituting g(x) into f(x), we get f×g = f(g(x)) = f(7+2x). Simplifying this expression, we get f×g = 3(7+2x)+½. Expanding and simplifying further, we get f×g = 21+6x+½. So, the correct answer is f(x)=6x²+22x+3½.

9) find (g∘f)(x) for x = 2 if f(x) = 2x +1 and g(x) = -x².

20

21

25

26

To find (g∘f)(x), we need to substitute the value of x=2 into f(x) first. f(2) = 2(2) + 1 = 5. Then, we substitute this value into g(x). g(5) = -(5)^2 = -25. Therefore, (g∘f)(2) = -25.

Explanation

To find (g∘f)(x), we need to substitute the value of x=2 into f(x) first. f(2) = 2(2) + 1 = 5. Then, we substitute this value into g(x). g(5) = -(5)^2 = -25. Therefore, (g∘f)(2) = -25.

10) An electrician charges a base fee of $70 plus $50 for each hour of work. Write a function that shows the amount the electrician charges for every he works.

The given function f(x)=70+50x represents the amount the electrician charges for every hour of work. The base fee of $70 is added to the product of $50 and the number of hours worked, x. This function calculates the total cost by multiplying the hourly rate by the number of hours worked and adding the base fee.

Explanation

The given function f(x)=70+50x represents the amount the electrician charges for every hour of work. The base fee of $70 is added to the product of $50 and the number of hours worked, x. This function calculates the total cost by multiplying the hourly rate by the number of hours worked and adding the base fee.

Submit