Question

Given f(x) = 2x − 5 and g(x) = 3x² + 5, and h(x) = 3x + 2, find:

1. (f)(4)

5. (f+h)(2)

2. (g)(-1)

3. (h)(4)

6. (f - g)(-3)

7. (g + h)(-2)

4. (f + g)(-2)​

Answer 1

see explanation

Explanation:

1

f(4) means what is the value of f(x) when x = 4

substitute x = 4 into f(x)

f(4) = 2(4) - 5 = 8 - 5= 3

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2

substitute x = - 1 into g(x)

g(- 1) = 3(- 1)² + 5 = 3(1) + 5 = 3 + 5 = 8

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3

substitute x = 4 into h(x)

h(4) = 3(4) + 2 = 12 + 2 = 14

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4

(f + g)(- 2)

= f(- 2) + g(- 2)

= 2(- 2) - 5 + 3(- 2)² + 5

= - 4 - 5 + 3(4) + 5

= - 9 + 12 + 5

= - 9 + 17

= 8

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5

(f + h)(2)

= f(2) + h(2)

= 2(2) - 5 + 3(2) + 2

= 4 - 5 + 6 + 2

= - 1 + 8

= 7

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6

(f - g)(- 3)

= f(- 3) - g(- 3)

= 2(- 3) - 5 - (3(- 3)² + 5)

= - 6 - 5 - ( 3(9) + 5)

= - 11 - ( 27 + 5)

= - 11 - ( 32)

= - 11 - 32

= - 43

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7

(g + h)(- 2)

= g(- 2) + h(- 2)

= 3(- 2)² + 5 + 3(- 2) + 2

= 3(4) + 5 - 6 + 2

= 12 + 5 - 4

= 17 - 4

= 13