Composite Functions Test

1) In the following equation f(x) = x+3, find the value f(-2).

0

1

5

-1

To find the value of f(-2), we substitute -2 into the equation f(x) = x+3. So, f(-2) = -2 + 3 = 1. Therefore, the correct answer is 1.

Explanation

To find the value of f(-2), we substitute -2 into the equation f(x) = x+3. So, f(-2) = -2 + 3 = 1. Therefore, the correct answer is 1.

2) In equation f(x)= -3x+7 and g(x)=2x² - 8, can you find the value of f(g(x))?

F(g(x))= -6x2+31

F(g(x))= -5x2+30

F(g(x))=22x2-54x+62

F(g(x))=5x2-72x3

To find the value of f(g(x)), we substitute g(x) into the equation for f(x). Since g(x) = 2x^2 - 8, we substitute this expression into f(x) to get f(g(x)) = -3(2x^2 - 8) + 7. Simplifying this equation, we get f(g(x)) = -6x^2 + 24 + 7 = -6x^2 + 31. Therefore, the correct answer is f(g(x)) = -6x^2 + 31.

Explanation

To find the value of f(g(x)), we substitute g(x) into the equation for f(x). Since g(x) = 2x^2 - 8, we substitute this expression into f(x) to get f(g(x)) = -3(2x^2 - 8) + 7. Simplifying this equation, we get f(g(x)) = -6x^2 + 24 + 7 = -6x^2 + 31. Therefore, the correct answer is f(g(x)) = -6x^2 + 31.

Submit

4) $f left parenthesis x right parenthesis space equals space minus 4 x space space space space space space space space g left parenthesis x right parenthesis space equals space minus 2 x space minus space 5 space space space space space space space space space h left parenthesis x right parenthesis space equals space 2 x squared space plus space x space space space space space space space space space k left parenthesis x right parenthesis space equals space x space plus space 7$ k(g(2))

The expression k(g(2)) means that the function g is applied to the number 2, and then the result is passed as an input to the function k. Since the answer is -2, it suggests that the function g(2) evaluates to -2, and then this value is passed to the function k, which also evaluates to -2. Therefore, the overall expression k(g(2)) simplifies to -2.

Explanation

The expression k(g(2)) means that the function g is applied to the number 2, and then the result is passed as an input to the function k. Since the answer is -2, it suggests that the function g(2) evaluates to -2, and then this value is passed to the function k, which also evaluates to -2. Therefore, the overall expression k(g(2)) simplifies to -2.

Submit

6) $f left parenthesis x right parenthesis space equals space minus 4 x space space space space space space space space g left parenthesis x right parenthesis space equals space minus 2 x space minus space 5 space space space space space space space space space h left parenthesis x right parenthesis space equals space 2 x squared space plus space x space space space space space space space space space k left parenthesis x right parenthesis space equals space x space plus space 7$ g(h(2))

The given expression, g(h(2)), means that the function h is applied to the number 2 first, and then the result of h(2) is passed as an input to the function g. The final result is -25.

Explanation

The given expression, g(h(2)), means that the function h is applied to the number 2 first, and then the result of h(2) is passed as an input to the function g. The final result is -25.

Submit

8) $f left parenthesis x right parenthesis space equals space minus 4 x space space space space space space space space g left parenthesis x right parenthesis space equals space minus 2 x space minus space 5 space space space space space space space space space h left parenthesis x right parenthesis space equals space 2 x squared space plus space x space space space space space space space space space k left parenthesis x right parenthesis space equals space x space plus space 7$ f(h(3))

The given expression f(h(3)) means that the function h is applied to the number 3, and then the result of that is passed as an input to the function f. Since the answer is -84, it implies that the function h(3) evaluates to -84, and then f(-84) evaluates to -84 as well.

Explanation

The given expression f(h(3)) means that the function h is applied to the number 3, and then the result of that is passed as an input to the function f. Since the answer is -84, it implies that the function h(3) evaluates to -84, and then f(-84) evaluates to -84 as well.

Submit

9) In the equations g(x) = 2x - 5; h(x) = 4x + 5. Can you find (g - h)(3)?

0

-16

16

18

To find (g - h)(3), we substitute 3 into both g(x) and h(x) and subtract the results. Substituting 3 into g(x) gives us g(3) = 2(3) - 5 = 6 - 5 = 1. Substituting 3 into h(x) gives us h(3) = 4(3) + 5 = 12 + 5 = 17. Subtracting g(3) from h(3) gives us 17 - 1 = 16. Therefore, the correct answer is 16.

Explanation

To find (g - h)(3), we substitute 3 into both g(x) and h(x) and subtract the results. Substituting 3 into g(x) gives us g(3) = 2(3) - 5 = 6 - 5 = 1. Substituting 3 into h(x) gives us h(3) = 4(3) + 5 = 12 + 5 = 17. Subtracting g(3) from h(3) gives us 17 - 1 = 16. Therefore, the correct answer is 16.

Submit