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Do you know how to find the composition of functions? Can you solve these function composition questions and answers in this quiz? Go ahead then and check how good you are at solving mathematics problems. In mathematics, the composition of functions is an operation that is written inside another function. It takes two functions f and generates a new function; we can say h in such a way that h(x) = g(f(x)). Here, you have to solve function composition problems. Let's see if you can do that or not.
Questions and Answers
1.
Find the value of f(6) in f(x)=x²+3x-2
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.
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2.
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.
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.
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3.
Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f×g.
A.
F(x)=6x²+21x+2½
B.
F(x)=6x²+22x+3½
C.
F(x)=5x²+20x+2½
D.
None of these
Correct Answer
B. 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.
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4.
Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f-g.
A.
F(x)=x-6½
B.
F(x)=x-5½
C.
F(x)=2x-6½
D.
F(x)=x+6½
Correct Answer
A. F(x)=x-6½
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.
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5.
Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f/g.
A.
F/g= (3x+1) /(7+2x)
B.
F/g= (3x+½) /(7+2x)
C.
F/g= (3x+½) /(6+2x)
D.
F/g= (3x-1) /(7+2x)
Correct Answer
B. F/g= (3x+½) /(7+2x)
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.
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6.
Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f ∘ g.
A.
F ∘ g= 7x+21 ½
B.
F ∘ g= 6x+21
C.
F ∘ g= 6x+21 ½
D.
None of these
Correct Answer
C. F ∘ g= 6x+21 ½
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.
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7.
Given functions f(x) = 3x+½ and g(x)= 7+2x. Find g ∘ f.
A.
G ∘ f=6x+8
B.
G ∘ f=6x+9
C.
G ∘ f=x+8
D.
G ∘ f=x-8
Correct Answer
A. G ∘ f=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.
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8.
Given functions f(x) = 3x+½ and g(x)= 7+2x. Find f+g.
A.
F+g=5x+7 ½
B.
F+g=x+7 ½
C.
F+g=5x+7
D.
F+g=5x-7 ½
Correct Answer
A. F+g=5x+7 ½
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.
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9.
For f(x) = 2x + 3 and g(x) = -x^{ 2} + 1, find (f _{o} g)(x)
find (g∘f)(x) for x = 2 if f(x) = 2x +1 and g(x) = -x^{2}.
A.
20
B.
21
C.
25
D.
26
Correct Answer
C. 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.
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